2022/05/09 更新

ナカヤマ　ユウ

NAKAYAMA Yu
*大学が定期的に情報更新している項目（その他は、researchmapの登録情報を転載）

• 場の量子論や超弦理論で生まれてきた最新の理論物理学の道具を使って、理論物理学の普遍的な枠組みを理解し、その理論的応用を考えることを研究テーマとする。具体的には、共形ブートストラップ法を用いた臨界現象の研究、ゲージ・重力対応に基づく量子重力理論と繰り込み群の研究など、ミクロな世界からマクロな世界まで統一的に理解したいと考えている。

• 担当科目*
2022年度
学内職務経歴*
• 2016年4月 - 現在
理学部   物理学科   准教授
• 2016年4月 - 現在
理学研究科   物理学専攻博士課程前期課程   准教授
• 2016年4月 - 現在
理学研究科   物理学専攻博士課程後期課程   准教授

### 研究分野

• 自然科学一般 / 素粒子、原子核、宇宙線、宇宙物理にする理論

### 経歴

• 2016年4月 - 現在
立教大学   理学研究科 物理学専攻博士課程前期課程   准教授

詳細を見る

• 2016年4月 - 現在
立教大学   理学研究科 物理学専攻博士課程後期課程   准教授

詳細を見る

• 2016年4月 - 現在
立教大学   理学部 物理学科   准教授

詳細を見る

### 学歴

• - 2007年3月
東京大学   理学系研究科

詳細を見る

国名： 日本国

• - 2007年3月
東京大学   理学系研究科

詳細を見る

国名： 日本国

• - 2002年3月
東京大学   理学部

詳細を見る

国名： 日本国

### 論文

• Yu Nakayama

2021年8月24日

詳細を見る

We construct a Weyl transverse diffeomorphism invariant theory of symmetric
teleparallel gravity by employing the Weyl compensator formalism. The
low-energy dynamics has a single spin two gravition without a scalar degree of
freedom. By construction, it is equivalent to the unimodular gravity (as well
as the Einstein gravity) at the non-linear level.

• Yu Nakayama

2021年8月5日

詳細を見る

The Gau\ss{} hypergeometric function shows a recursive structure which
resembles those found in conformal blocks. We compare it with the recursive
structure of the conformal block in boundary/crosscap conformal field theories
that is obtained from the representation theory. We find that the pole
structure perfectly agrees but the recursive structure in the Gau\ss{}
hypergeometric function is slightly off-shell".

• Yu Nakayama

2021年4月28日

詳細を見る

The supersymmetric Lee-Yang model is arguably the simplest interacting
supersymmetric field theory in two dimensions, albeit non-unitary. A natural
question is if there is an analogue of supersymmetric Lee-Yang fixed point in
higher dimensions. The absence of any $\mathbb{Z}_2$ symmetry (except for
fermion numbers) makes it impossible to approach it by using perturbative
$\epsilon$ expansions. We find that the truncated conformal bootstrap suggests
that candidate fixed points obtained by the dimensional continuation from two
dimensions annihilate below three dimensions, implying that there is no
supersymmetric Lee-Yang fixed point in three dimensions. We conjecture that the
corresponding phase transition, if any, will be the first order transition.

• Tsubasa Yuki, Yu Nakayama

2021年3月2日

詳細を見る

We investigate an alternative quantization of R-NS string theory. In the
alternative quantization, we define the distinct vacuum for the left-moving
mode and the right-moving mode by exchanging the role of creation operators and
annihilation operators in the left-moving sector. The resulting string theory
has only a finite number of propagating degrees of freedom. We show that an
appropriate choice of the GSO projection makes the theory tachyon free. The
spectrum coincides with the massless sector of type IIA or type IIB superstring
theory without any massive excitations.

• Yu Nakayama, Yusuke Nishida

2020年10月28日

詳細を見る

Surface growth governed by the Kardar-Parisi-Zhang (KPZ) equation in
dimensions higher than two undergoes a roughening transition from smooth to
rough phases with increasing the nonlinearity. It is also known that the KPZ
equation can be mapped onto quantum mechanics of attractive bosons with a
contact interaction, where the roughening transition corresponds to a binding
transition of two bosons with increasing the attraction. Such critical bosons
in three dimensions actually exhibit the Efimov effect, where a three-boson
coupling turns out to be relevant under the renormalization group so as to
break the scale invariance down to discrete one. On the basis of these facts
linking the two distinct subjects in physics, we predict that the KPZ
roughening transition in three dimensions shows either the discrete scale
invariance or no intrinsic scale invariance.

• Yu Nakayama

2020年9月30日

詳細を見る

We study anomalous hydrodynamics with a dyonic charge. We show that the local
second law of thermodynamics constrains the structure of the anomaly in
addition to the structure of the hydrodynamic constitutive equations. In
particular, we show that not only the usual $E\cdot B$ term but also $E^2 -B^2$
term should be present in the anomaly with a specific coefficient for the local
entropy production to be positive definite.

• Yu Nakayama

2020年6月9日

詳細を見る

There exists a certain argument that in even dimensions, scale invariant
quantum field theories are conformal invariant. We may try to extend the
argument in $2n + \epsilon$ dimensions, but the naive extension has a small
loophole, which indeed shows an obstruction in non-linear sigma models in
$2+\epsilon$ dimensions. Even though it could have failed due to the loophole,
we show that scale invariance does imply conformal invariance of non-linear
sigma models in $2+\epsilon$ dimension from the seminal work by Perelman on the
Ricci flow.

• Yu Nakayama

2020年4月17日

詳細を見る

Based on the numerical conformal bootstrap bound, we show that the
arbitrarily small Reissner-Nordstr\"om black hole in AdS space-time is
inconsistent with holography unless the energy spectrum is modified quantum
mechanically or it is unstable as indicated by the weak gravity conjecture.

• Chang-Tse Hsieh, Yu Nakayama, Yuji Tachikawa

2020年2月27日

詳細を見る

We show that there is a fermionic minimal model, i.e. a 1+1d conformal field
theory which contains operators of half-integral spins in its spectrum, for
each $c=1-6/m(m+1)$, $m\ge 3$. This generalizes the Majorana fermion for
$c=1/2$, $m=3$ and the smallest $\mathcal{N}{=}1$ supersymmetric minimal model
for $c=7/10$, $m=4$. We provide explicit Hamiltonians on Majorana chains
realizing these fermionic minimal models.

• Koichiro Nakagawa, Yu Nakayama

2020年2月4日

詳細を見る

In CP-violating conformal field theories in four dimensions, the Pontryagin
density can appear in the Weyl anomaly. The Pontryagin density in the Weyl
anomaly is consistent, but it has a peculiar feature that the parent
three-point function of the energy-momentum tensor can violate CP only
(semi-)locally. In this paper, we study the supersymmetric completion of the
Pontryagin density in the Weyl anomaly, where the central charge $c$
effectively becomes a complex number. The supersymmetry suggests that it
accompanies the graviphoton $\theta$ term associated with the R-symmetry
gauging in the Weyl anomaly. It also accompanies new CP-violating terms in the
R-current anomaly. While there are no conclusive perturbative examples of
CP-violating super Weyl anomaly, we construct explicit supersymmetric dilaton
effective action which generates these anomalies.

• Yu Nakayama

2020年1月30日

詳細を見る

Similarly to the bosonic Liouville theory, the $\mathcal{N}=2$ supersymmetric
Liouville theory was conjectured to be equipped with the duality that exchanges
the superpotential and the K\"ahler potential. The conjectured duality,
however, seems to suffer from a mismatch of the preserved symmetries. More than
fifteen years ago, when I was a student, my supervisor Tohru Eguchi gave a
beautiful resolution of the puzzle when the supersymmetry is enhanced to
$\mathcal{N}=4$ based on his insight into the underlying geometric structure of
the $A_1$ singularity. I will review his unpublished but insightful idea and
present our attempts to extend it to more general cases.

• Yu Nakayama

2019年12月26日

詳細を見る

How large can anomalous dimensions be in conformal field theories? What can
we do to attain larger values? One attempt to obtain large anomalous dimensions
efficiently is to use the Pauli exclusion principle. Certain operators
constructed out of constituent fermions cannot form bound states without
introducing non-trivial excitations. To assess the efficiency of this
mechanism, we compare them with the numerical conformal bootstrap bound as well
as with other interacting field theory examples. In two dimensions, it turns
out to be the most efficient: it saturates the bound and is located at the
(second) kink. In higher dimensions, it more or less saturates the bound but it
may be slightly inside.

• Ariel Edery, Yu Nakayama

2019年8月23日

詳細を見る

We show that a critical condition exists in four dimensional scale invariant
gravity given by the pure quadratic action $\beta \,C_{\mu\nu\sigma\rho} C^{\mu\nu\sigma \rho} + \alpha \,R^2$ where $C^{\mu}_{\,\,\nu \sigma \rho}$ is
the Weyl tensor, $R$ is the Ricci scalar and $\beta$ and $\alpha$ are
dimensionless parameters. The critical condition in a dS or AdS background is
$\beta =6 \alpha$. This leads to critical gravity where the massive spin two
physical ghost becomes a massless spin two graviton. In contrast to the
original work on critical gravity, no Einstein gravity with a cosmological
constant is added explicitly to the higher-derivative action. The critical
condition is obtained in two independent ways. In the first case, we show the
equivalence between the initial action and an action containing Einstein
gravity, a cosmological constant, a massless scalar field plus Weyl squared
gravity. The scale invariance is spontaneously broken. The linearized
condition $\beta=6\alpha$. In the second case, we work directly with the
original quadratic action. After a suitable field redefinition, where the
metric perturbation is traceless and transverse, we obtain linearized equations
about a dS or AdS background that yield the critical condition $\beta= 6\alpha$. As in the first case, we also obtain a propagating massless scalar
field. Substituting $\beta=6\alpha$ into the energy and entropy formula for the
Schwarzschild and Kerr AdS or dS black hole in higher-derivative gravity yields
zero, the same value obtained in the original work on critical gravity. We
discuss the role of boundary conditions in relaxing the $\beta=6\alpha$
condition.

• Yu Nakayama

2019年6月19日

詳細を見る

We study conformal properties of local terms such as contact terms and
semi-local terms in correlation functions of a conformal field theory. Not all
of them are universal observables but they do appear in physically important
correlation functions such as (anomalous) Ward-Takahashi identities or
Schwinger-Dynson equations. We develop some tools such as embedding space delta
functions and effective action to examine conformal invariance of these local
terms.

• Yu Nakayama

2019年5月14日

詳細を見る

Very special $T\bar{J}$ deformations of a conformal field theory are
irrelevant deformations that break the Lorentz symmetry but preserve the
twisted Lorentz symmetry. We construct a holographic description of very
special $T\bar{J}$ deformations. We give a holographic recipe to study the
double trace as well as single trace deformations. The former is obtained from
the change of the boundary condition while the latter is obtained from the
change of the supergravity background.

• Ariel Edery, Yu Nakayama

2019年2月21日

詳細を見る

Pure $R^2$ gravity has been shown to be equivalent to Einstein gravity with
non-zero cosmological constant and a massless scalar field. We show that the
Palatini formulation of pure $R^2$ gravity is equivalent to Einstein gravity
with non-zero cosmological constant as before but with no massless scalar
field. This is an important new development because the massless scalar field
is not readily identifiable with any known particle in nature or unknown
particles like cold dark matter which are expected to be massive. We then
include a non-minimally coupled Higgs field as well as fermions to discuss how
the rest of the standard model fields fit into this paradigm. With Higgs field,
Weyl invariance is maintained by using a hybrid formalism that includes both
the Palatini curvature scalar $\mathcal{R}$ and the usual Ricci scalar $R$

• Yu Nakayama

2019年2月14日

詳細を見る

While the argument by Zamolodchikov and Polchinski suggests global conformal
invariance implies Virasoro invariance in two-dimensional unitary conformal
field theories with discrete dilatation spectrum, it is not the case in more
general situations without these assumptions. We indeed show that almost all
the globally conformal invariant differential equations in two dimensions are
neither Virasoro invariant nor Weyl invariant. The only exceptions are the
higher spin conservation laws, conformal Killing tensor equations and the
Laplace equation of a conformal scalar.

• Yu Nakayama

2018年11月6日

詳細を見る

We study a very special class of $T\bar{J}$ deformations of conformal field
theories in two dimensions. While the deformations break the Lorentz symmetry,
they preserve the twisted Lorentz symmetry. The resulting theory has
right-moving Virasoro as well as left-moving translation and left-moving
(chiral) scale symmetry without left-moving special conformal symmetry (nor
left-moving Virasoro symmetry). As in the original $T\bar{J}$ deformations,
they may be regarded as an operator dependent non-local change of coordinates.
We show concrete examples based on worldsheet string theory and discuss how the
non-unitary nature enables us to circumvent various no-go theorems.

• Natan Andrei, Agnese Bissi, Matthew Buican, John Cardy, Patrick Dorey, Nadav Drukker, Johanna Erdmenger, Daniel Friedan, Dmitri Fursaev, Anatoly Konechny, Charlotte Kristjansen, Isao Makabe, Yu Nakayama, Andy O'Bannon, Robert Parini, Brandon Robinson, Shinsei Ryu, Cornelius Schmidt-Colinet, Volker Schomerus, Christoph Schweigert, Gerard Watts

2018年10月12日

詳細を見る

Proceedings of the workshop "Boundary and Defect Conformal Field Theory: Open
Problems and Applications," Chicheley Hall, Buckinghamshire, UK, 7-8 Sept.
2017.

• Yu Nakayama

2018年7月24日

詳細を見る

We study holographic dual descriptions of very special conformal field
theories with the T(2) symmetry. After constructing solutions in effective five
dimensional Einstein gravity coupled with massive two-form fields, we uplift
them to the ten dimensional type IIB supergravity, via a consistent truncation
ansatz, to derive new analytical solutions in string theory. From the
Kaluza-Klein ansatz in terms of the internal Sasaki-Einstein space, we obtain
their field theory interpretation with concrete realizations in a large class
of holographic $\mathcal{N}=1$ supersymmetric conformal field theories. Null
compactification of these theories yields holographic dual descriptions of
non-relativistic critical systems with translational invariance but without
rotational invariance such as the ones induced from a constant electromagnetic
field.

• Ariel Edery, Yu Nakayama

2018年7月18日

詳細を見る

The pure $R^2$ gravity is equivalent to Einstein gravity with cosmological
constant and a massless scalar field and it further possesses the so-called
restricted Weyl symmetry which is a symmetry larger than scale symmetry. To
incorporate matter, we consider a restricted Weyl invariant action composed of
pure $R^2$ gravity, SU(2) Yang-Mills fields and a non-minimally coupled
massless Higgs field (a triplet of scalars). When the restricted Weyl symmetry
is spontaneously broken, it is equivalent to an Einstein-Yang-Mills-Higgs
(EYMH) action with a cosmological constant and a massive Higgs non-minimally
coupled to gravity i.e. via a term $\tilde{\xi} R |\Phi|^2$. When the
restricted Weyl symmetry is not spontaneously broken, linearization about
Minkowski space-time does not yield gravitons in the original $R^2$ gravity and
hence it does not gravitate. However, we show that in the broken gauge sector
of our theory, where the Higgs field acquires a non-zero vacuum expectation
value, Minkowski space-time is a viable gravitating background solution. We
then obtain numerically gravitating magnetic monopole solutions for non-zero
coupling constant $\tilde{\xi}=1/6$ in three different backgrounds: Minkowski,
anti-de Sitter (AdS) and de Sitter (dS), all of which are realized in our
restricted Weyl invariant theory.

• Yu Nakayama

2018年4月9日

詳細を見る

The Wess-Zumino consistency condition allows more exotic forms of anomalies
than those we usually encounter. For example in two-dimensional conformal field
theories in the curved background with space-time dependent coupling constant
$\lambda^i(x)$, a $U(1)$ current could possess anomalous divergence of the form
$D^\mu J_\mu = \tilde{c} R + \chi_{ij} \partial^\mu \lambda^i \partial_\mu\lambda_j + \tilde{\chi}_{ij} \epsilon^{\mu\nu} \partial_\mu \lambda^i \partial_\nu \lambda^j + \cdots$. Another example is the CP odd
Pontryagin density in four-dimensional Weyl anomaly. We could, however, argue
that they are impossible in conformal field theories because they cannot
correspond to any (unregularized) conformally invariant correlation functions.
We find that this no-go argument may be a red herring. We show that some of
these impossible anomalies avoid the no-go argument because they are not
primary operators, and the others circumvent it because they are realized as
semi-local terms as is the case with the conformally invariant Green-Schwartz
mechanism and in the higher dimensional analogue of Liouville or linear dilaton
theory.

• Yu Nakayama

2018年2月19日

詳細を見る

Cohen and Glashow argued that very special conformal field theories of a
particular kind (i.e. with HOM(2) or SIM(2) invariance) cannot be constructed
within the framework of local field theories. We, however, show examples of
local construction by using non-linear realization. We further construct linear
realization from the topological twist at the cost of unitarity. To demonstrate
the ubiquity of our idea, we also present corresponding holographic models.

• Chika Hasegawa, Yu Nakayama

2018年1月27日

詳細を見る

We solve the two-point function of the lowest dimensional scalar operator in
the critical $\phi^4$ theory on $4-\epsilon$ dimensional real projective space
in three different methods. The first is to use the conventional perturbation
theory, and the second is to impose the crosscap bootstrap equation, and the
third is to solve the Schwinger-Dyson equation under the assumption of
conformal invariance. We find that the three methods lead to mutually
consistent results but each has its own advantage.

• Yu Nakayama

2017年11月17日

詳細を見る

Once we put a quantum field theory on a curved manifold, it is natural to
further assume that coupling constants are position dependent. The position
dependent coupling constants then provide an extra contribution to the Weyl
anomaly so that we may attempt to cancel the entire Weyl anomaly on the curved
manifold. We show that such a cancellation is possible for constant Weyl
transformation or infinitesimal but generic Weyl transformation in two and four
dimensional conformal field theories with exactly marginal deformations. When
the Weyl scaling factor is annihilated by conformal powers of Laplacian (e.g.
by Fradkin-Tseytlin-Riegert-Paneitz operator in four dimensions), the
cancellation persists even at the finite order thanks to a nice mathematical
property of the $Q$-curvature under the Weyl transformation.

• Hosho Katsura, Hajime Moriya, Yu Nakayama

2017年10月12日

詳細を見る

We study a supersymmetric fermion lattice model defined by Hermann Nicolai.
We show that its infinitely many classical supersymmetric ground states are
associated to breakdown of hidden local supersymmetries.

• Yu Nakayama

2017年7月18日

詳細を見る

Cohen and Glashow introduced the notion of very special relativity as viable
space-time symmetry of elementary particle physics. As a natural generalization
of their idea, we study the subgroup of the conformal group, dubbed very
special conformal symmetry, which is an extension of the very special
relativity. We classify all of them and construct field theory examples as well
as holographic realization of the very special conformal field theories.

• K. -I. Ishikawa, Y. Iwasaki, Yu Nakayama, T. Yoshie

2017年6月25日

詳細を見る

We investigate the nature of the chiral phase transition in the massless
two-flavor QCD using the renormalization group improved gauge action and the
Wilson quark action on $32^3\times 16$, $24^3\times 12$, and $16^3\times 8$
lattices. We calculate the spacial and temporal propagators of the iso-triplet
mesons in the pseudo-scalar ($PS$), scalar ($S$), vector ($V$) and axial-vector
($AV$) channels on the lattice of three sizes. We first verify that the RG
scaling is excellently satisfied for all cases. This is consistent with the
claim that the chiral phase transition is second order. Then we compare the
spacial and temporal effective masses between the axial partners, i.e. $PS$ vs
$S$ and $V$ vs $AV$, on each of the three size lattices. We find the effective
masses of all of six cases for the axial partners agree remarkably. This is
consistent with the claim that at least $Z_4$ subgroup of the $U_A(1)$ symmetry
in addition to the $SU_A(2)$ symmetry is recovered at the chiral phase
transition point.

• Yu Nakayama

2017年5月8日

詳細を見る

Recent programs on conformal bootstrap suggest an empirical relationship
between the existence of non-trivial conformal field theories and non-trivial
features such as a kink in the unitarity bound of conformal dimensions in the
conformal bootstrap equations. We report the existene of non-trivial kinks in
the unitarity bound of scalar operators in the adjoint representation of the
$SU(N)$ symmetric conformal field theories. They have interesting properties
(1) the kinks exist in $d<6$ dimensions (2) the location of kinks are when the
unitarity bound hits the space-time dimension $d$ (3) there exists a "conformal
window" of $N<N_*$, where $N_* \sim 15$ in $d=4$ and $N_* \sim 20$ in $d=5$.

• K. -I. Ishikawa, Y. Iwasaki, Yu Nakayama, T. Yoshie

2017年4月11日

詳細を見る

We investigate the nature of the chiral phase transition in the massless
two-flavor QCD using the renormalization group improved gauge action and the
Wilson quark action on $32^3\times 16$, $24^3\times 12$, and $16^3\times 8$
lattices. Based on the renormalization group equation, we derive the scaling
relation for the effective masses of mesons at the chiral phase transition
point. If the chiral phase transition is second order, the effective masses as
a function of the rescaled time/space do not depend on the lattice size and
show the universal behavior. We find that our numerical simulations on the
three sizes of lattices are excellently on the scaling curves, which is
consistent with the second order phase transition.

• Yu Nakayama

2017年2月8日

詳細を見る

There is no known obstructions, but we have not been aware of any concrete
examples, either. The Wess-Zumino consistency condition for the conformal
anomaly says that $a$ cannot change but does not say anything about $c$. In
supersymmetric models, both $a$ and $c$ are determined from the triangle
t'Hooft anomalies and the unitarity demands that both must be fixed, so the
unitary supersymmetric conformal field theories do not admit such a
possibility. Given this field theory situation, we construct an effective
AdS/CFT model without supersymmetry in which $c$ changes under exactly marginal
deformations. So, yes, we can.

• Noriaki Sannomiya, Hosho Katsura, Yu Nakayama

2016年12月7日

詳細を見る

We introduce a lattice fermion model in one spatial dimension with
supersymmetry (SUSY) but without particle number conservation. The Hamiltonian
is defined as the anticommutator of two nilpotent supercharges $Q$ and
$Q^\dagger$. Each supercharge is built solely from spinless fermion operators
and depends on a parameter $g$. The system is strongly interacting for small
$g$, and in the extreme limit $g=0$, the number of zero-energy ground states
grows exponentially with the system size. By contrast, in the large-$g$ limit,
the system is non-interacting and SUSY is broken spontaneously. We study the
model for modest values of $g$ and show that under certain conditions
spontaneous SUSY breaking occurs in both finite and infinite chains. We analyze
the low-energy excitations both analytically and numerically. Our analysis
suggests that the Nambu-Goldstone fermions accompanying the spontaneous SUSY
breaking have cubic dispersion at low energies.

• Yu Nakayama

2016年11月30日

詳細を見る

There is a dilemma in constructing interacting scale invariant but not
conformal invariant Euclidean field theories. On one hand, scale invariance
without conformal invariance seems more generic by requiring only a smaller
symmetry. On the other hand, the existence of a non-conserved current with
exact scaling dimension $d-1$ in $d$ dimensions seems to require extra
fine-tuning. To understand the competition better, we explore some examples
without the reflection positivity. We show that a theory of elasticity (a.k.a
Riva-Cardy theory) coupled with massless fermions in $d=4-\epsilon$ dimensions
does not possess an interacting scale invariant fixed point except for unstable
(and unphysical) one with an infinite coefficient of compression. We do,
however, find interacting scale invariant but non-conformal field theories in
gauge fixed versions of the Banks-Zaks fixed points in $d=4$ dimensions.

• Chika Hasegawa, Yu Nakayama

2016年11月19日

詳細を見る

We use a compatibility between the conformal symmetry and the equations of
motion to solve the one-point function in the critical $\phi^3$-theory (a.k.a
the critical Lee-Yang model) on the $d = 6 - \epsilon$ dimensional real
projective space to the first non-trivial order in the $\epsilon$-expansion. It
reproduces the conventional perturbation theory and agrees with the numerical
conformal bootstrap result.

• Yu Nakayama

2016年8月8日

詳細を見る

We show that eleven dimensional supergravity in Euclidean signature admits an
exact classical solution with isometry corresponding to a three dimensional
scale invariant field theory without conformal invariance. We also construct
the holographic renormalization group flow that connects the known UV conformal
fixed point and the new scale invariant but not conformal fixed point. In view
of holography, the existence of such classical solutions suggests that the
topologically twisted M2-brane gauge theory possesses a scale invariant but not
conformal phase.

• Noriaki Sannomiya, Hosho Katsura, Yu Nakayama

2016年6月13日

詳細を見る

We study a model of interacting spinless fermions in a one dimensional
lattice with supersymmetry (SUSY). The Hamiltonian is given by the
anti-commutator of two supercharges $Q$ and $Q^\dagger$, each of which is
comprised solely of fermion operators and possesses one adjustable parameter
$g$. When the parameter $g$ vanishes, the model is identical to the one studied
by Nicolai [H. Nicolai, J. Phys. A: Math. Gen. \textbf{9}, 1497 (1976)], where
the zero-energy ground state is exponentially degenerate. On the other hand, in
the large-$g$ limit the model reduces to the free-fermion chain with a
four-fold degenerate ground state. We show that for finite chains SUSY is
spontaneously broken when $g > 0$. We also rigorously prove that for
sufficiently large $g$ the ground-state energy density is nonvanishing in the
infinite-volume limit. We further analyze the nature of the low-energy
excitations by employing various techniques such as rigorous inequalities,
exact numerical diagonalization, and renormalization group method with
bosonization. The analysis reveals that the low-energy excitations are
described by massless Dirac fermions (or Thirring fermions more generally),
which can be thought of as Nambu-Goldstone fermions from the spontaneous SUSY
breaking.

• Yu Nakayama

2016年6月7日

詳細を見る

Euclidean field theories admit more general deformations than usually
discussed in quantum field theories because of mixing between rotational
symmetry and internal symmetry (a.k.a topological twist). Such deformations may
be relevant, and if the subsequent renormalization group flow leads to a
non-trivial fixed point, it generically gives rise to a scale invariant
Euclidean field theory without conformal invariance. Motivated by an ansatz
studied in cosmological models some time ago, we develop a holographic dual
description of such renormalization group flows in the context of AdS/CFT. We
argue that the non-trivial fixed points require fine-tuning of the bulk theory
in general, but remarkably we find that the $O(3)$ Yang-Mills theory coupled
with the four-dimensional Einstein gravity in the minimal manner supports such
a background with the Euclidean AdS metric.

• Yu Nakayama

2016年5月13日

詳細を見る

The recent work by Iha et al shows an upper bound on mass anomalous dimension
$\gamma_m$ of multi-flavor massless QCD at the renormalization group fixed
point from the conformal bootstrap in $SU(N_F)_V$ symmetric conformal field
theories under the assumption that the fixed point is realizable with the
lattice regularization based on staggered fermions. We show that the almost
identical but slightly stronger bound applies to the regularization based on
Wilson fermions (or domain wall fermions) by studying the conformal bootstrap
in $SU(N_f)_L \times SU(N_f)_R$ symmetric conformal field theories. For
$N_f=8$, our bound implies $\gamma_m < 1.31$ to avoid dangerously irrelevant
operators that are not compatible with the lattice symmetry.

• Yu Nakayama, Hirosi Ooguri

2016年5月2日

詳細を見る

In a weakly coupled gravity theory in the anti-de Sitter space, local states
in the bulk are linear superpositions of Ishibashi states for a crosscap in the
dual conformal field theory. The superposition structure can be constrained
either by the microscopic causality in the bulk gravity or the bootstrap
condition in the boundary conformal field theory. We show, contrary to some
expectation, that these two conditions are not compatible to each other in the
weak gravity regime. We also present an evidence to show that bulk local states
in three dimensions are not organized by the Virasoro symmetry.

• Yu Nakayama

2016年4月4日

詳細を見る

The theory of elasticity (a.k.a. Riva-Cardy model) has been regarded as an
example of scale invariant but not conformal field theories. We argue that in
$d=2$ dimensions, the theory has hidden global conformal symmetry of
$SL(2,\mathbb{R}) \times SL(2,\mathbb{R})$ without its Virasoro extension. More
precisely, we can embed all the correlation functions of the displacement
vector into a global conformal field theory with four-derivative action in
terms of two scalar potential variables, which necessarily violates the
reflection positivity. The energy-momentum tensor for the potential variables
cannot be improved to become traceless so that it does not show the Virasoro
symmetry even with the existence of global special conformal current.

• Yu Nakayama, Tomoki Ohtsuki

2016年2月23日

詳細を見る

We use the conformal bootstrap program to derive necessary conditions for
emergent symmetry enhancement from discrete symmetry (e.g. $\mathbb{Z}_n$) to
continuous symmetry (e.g. $U(1)$) under the renormalization group flow. In
three dimensions, in order for $\mathbb{Z}_2$ symmetry to be enhanced to $U(1)$
symmetry, the conformal bootstrap program predicts that the scaling dimension
of the order parameter field at the infrared conformal fixed point must satisfy
$\Delta_1 > 1.08$. We also obtain the similar conditions for $\mathbb{Z}_3$
symmetry with $\Delta_{1} > 0.580$ and $\mathbb{Z}_4$ symmetry with $\Delta_1 > 0.504$ from the simultaneous conformal bootstrap analysis of multiple
four-point functions. Our necessary conditions impose severe constraints on
many controversial physics such as the chiral phase transition in QCD, the
deconfinement criticality in N\'eel-VBS transitions and anisotropic
deformations in critical $O(n)$ models. In some cases, we find that the
conformal bootstrap program dashes hopes of emergent symmetry enhancement
proposed in the literature.

• Yu Nakayama

2016年1月25日

詳細を見る

Given a conformal data on a flat Euclidean space, we use crosscap conformal
bootstrap equations to numerically solve the Lee-Yang model as well as the
critical Ising model on a three-dimensional real projective space. We check the
rapid convergence of our bootstrap program in two-dimensions from the exact
solutions available. Based on the comparison, we estimate that our systematic
error on the numerically solved one-point functions of the critical Ising model
on a three-dimensional real projective space is less than one percent. Our
method opens up a novel way to solve conformal field theories on non-trivial
geometries.

• K. -I. Ishikawa, Y. Iwasaki, Yu Nakayama, T. Yoshie

2015年11月11日

詳細を見る

We investigate the properties of quarks and gluons above the chiral phase
transition temperature $T_c,$ using the RG improved gauge action and the Wilson
quark action with two degenerate quarks mainly on a $32^3\times 16$ lattice. In
the one-loop perturbation theory, the thermal ensemble is dominated by the
gauge configurations with effectively $Z(3)$ center twisted boundary
conditions, making the thermal expectation value of the spatial Polyakov loop
take a non-trivial $Z(3)$ center. This is in agreement with our lattice
simulation of high temperature QCD. We further observe that the temporal
propagator of massless quarks at extremely high temperature $\beta=100.0 \, (T \simeq10^{58} T_c)$ remarkably agrees with the temporal propagator of free
quarks with the $Z(3)$ twisted boundary condition for $t/L_t \geq 0.2$, but
differs from that with the $Z(3)$ trivial boundary condition. As we increase
the mass of quarks $m_q$, we find that the thermal ensemble continues to be
dominated by the $Z(3)$ twisted gauge field configurations as long as $m_q \le 3.0 \, T$ and above that the $Z(3)$ trivial configurations come in. The
transition is essentially identical to what we found in the departure from the
conformal region in the zero-temperature many-flavor conformal QCD on a finite
lattice by increasing the mass of quarks. We argue that the behavior is
consistent with the renormalization group analysis at finite temperature.

• Shinsuke Kawai, Yu Nakayama

2015年9月15日

詳細を見る

Assuming gauge/gravity correspondence we study reheating of the Universe
using its holographic dual. Inflaton decay and thermalisation of the decay
products correspond to collapse of a spherical shell and formation of a
blackhole in the dual anti-de Sitter (AdS) spacetime. The reheating temperature
is computed as the Hawking temperature of the developed blackhole probed by a
dynamical boundary, and is determined by the inflaton energy density and the
AdS radius, with corrections from the dynamics of the shell collapse. For given
initial energy density of the inflaton field the holographic model gives
significantly lower reheating temperature than the instant reheating scenario,
while it is shown to be safely within phenomenological bounds.

• Yu Nakayama, Yasunori Nomura

2015年9月5日

詳細を見る

We study implications of the weak gravity conjecture in the AdS/CFT
correspondence. Unlike in Minkowski spacetime, AdS spacetime has a physical
length scale, so that the conjecture must be generalized with an additional
parameter. We discuss possible generalizations and translate them into the
language of dual CFTs, which take the form of inequalities involving the
dimension and charge of an operator as well as the current and energy-momentum
tensor central charges. We then test these inequalities against various CFTs to
see if they are universally obeyed by all the CFTs. We find that certain CFTs,
such as supersymmetric QCDs, do not satisfy them even in the large $N$ limit.
This does not contradict the conjecture in AdS spacetime because the theories
violating them are either unlikely or unclear to have weakly coupled
gravitational descriptions, but it suggests that the CFT inequalities obtained
here by naive translations do not apply beyond the regime in which weakly
coupled gravitational descriptions are available.

• Yu Nakayama, Hirosi Ooguri

2015年7月15日

詳細を見る

We formulate a minimum requirement for CFT operators to be localized in the
dual AdS. In any spacetime dimensions, we show that a general solution to the
requirement is a linear superposition of operators creating spherical
boundaries in CFT, with the dilatation by the imaginary unit from their
centers. This generalizes the recent proposal by Miyaji et al. for bulk local
operators in the three dimensional AdS. We show that Ishibashi states for the
global conformal symmetry in any dimensions and with the imaginary dilatation
obey free field equations in AdS and that incorporating bulk interactions
require their superpositions. We also comment on the recent proposals by Kabat
et al., and by H. Verlinde.

• Yu Nakayama

2015年6月17日

詳細を見る

Gauging extra matter is a common way to couple two CFTs discontinuously. We
may consider gauging matter by strongly coupled gauge theories at criticality
rather than by weakly coupled (asymptotic free) gauge theories. It often
triggers relevant deformations and possibly leads to a non-trivial fixed point.
In many examples such as the IR limit of SQCDs (and their variants), the
relevant RG flow induced by this strong gauging makes the total central charge
$a$ increase rather than decrease compared with the sum of the original
decoupled CFTs. The dilaton effective field theory argument given by
Komargodski and Schwimmer does not apply because strong gauging is not a simple
deformation by operators in the original two decoupled CFTs and it may not be
UV complete. When the added matter is vector-like, one may emulate strong
gauging in a UV completed manner by decoupling of ghost matter. While the UV
completed description makes the dilaton effective field theory argument
possible, due to the non-unitarity, we cannot conclude the positivity of the
central charge difference in accordance with the observations in various
examples that show the contrary.

• K. -I. Ishikawa, Y. Iwasaki, Yu Nakayama, Y. Yoshie

2015年3月9日

詳細を見る

We propose a novel RG method to specify the location of the IR fixed point in
lattice gauge theories and apply it to the $SU(3)$ gauge theories with $N_f$
fundamental fermions. It is based on the scaling behavior of the propagator
through the RG analysis with a finite IR cut-off, which we cannot remove in the
conformal field theories in sharp contrast with the confining theories. The
method also enables us to estimate the anomalous mass dimension in the
continuum limit at the IR fixed point. We perform the program for $N_f=16, 12, 8$ and $N_f=7$ and indeed identify the location of the IR fixed points in all
cases.

• Yu Nakayama

2015年2月25日

詳細を見る

The bulk locality in the constructive holographic renormalization group
requires miraculous cancellations among various local renormalization group
functions. The cancellation is not only from the properties of the spectrum but
from more detailed aspects of operator product expansions in relation to
conformal anomaly. It is remarkable that one-loop computation of the universal
local renormalization group functions in the weakly coupled limit of the
$\mathcal{N}=4$ super Yang-Mills theory fulfils the necessary condition for the
cancellation in the strongly coupled limit in its $SL(2,\mathbf{Z})$ duality
invariant form. From the consistency between the quantum renormalization group
and the holographic renormalization group, we determine some unexplored local
renormalization group functions (e.g. diffusive term in the beta function for
the gauge coupling constant) in the strongly coupled limit of the planar
$\mathcal{N}=4$ super Yang-Mills theory.

• Ariel Edery, Yu Nakayama

2015年2月20日

詳細を見る

Recently, it has been pointed out that dimensionless actions in four
dimensional curved spacetime possess a symmetry which goes beyond scale
invariance but is smaller than full Weyl invariance. This symmetry was dubbed
{\it restricted Weyl invariance}. We show that starting with a restricted Weyl
invariant action that includes a Higgs sector with no explicit mass, one can
generate the Einstein-Hilbert action with cosmological constant and a Higgs
mass. The model also contains an extra massless scalar field which couples to
the Higgs field (and gravity). If the coupling of this extra scalar field to
the Higgs field is negligibly small, this fixes the coefficient of the
nonminimal coupling $R \Phi^2$ between the Higgs field and gravity. Besides the
Higgs sector, all the other fields of the standard model can be incorporated
into the original restricted Weyl invariant action.

• Yu Nakayama

2015年1月9日

詳細を見る

To explore the possibility of self-organized criticality, we look for CFTs
without any relevant scalar deformations (a.k.a dead-end CFTs) within
power-counting renormalizable quantum field theories with a weakly coupled
Lagrangian description. In three dimensions, the only candidates are pure
(Abelian) gauge theories, which may be further deformed by Chern-Simons terms.
In four dimensions, we show that there are infinitely many non-trivial
candidates based on chiral gauge theories. Using the three-loop beta functions,
we compute the gap of scaling dimensions above the marginal value, and it can
be as small as $\mathcal{O}(10^{-5})$ and robust against the perturbative
corrections. These classes of candidates are very weakly coupled and our
perturbative conclusion seems difficult to refute. Thus, the hypothesis that
non-trivial dead-end CFTs do not exist is likely to be false in four
dimensions.

• Takeo Inami, Yoji Koyama, Yu Nakayama, Mariko Suzuki

2014年12月7日

詳細を見る

There has been a proposal that infrared quantum effects of massless
interacting field theories in de-Sitter space may provide time-dependent
screening of the cosmological constant. As a concrete model of the proposal, we
study the three loop corrections to the energy-momentum tensor of massless
$\lambda \phi^4$ theory in the background of classical Liouville gravity in
$D=2$ dimensional de-Sitter space. We find that the cosmological constant is
screened in sharp contrast to the massless $\lambda \phi^4$ theory in $D=4$
dimensions due to the sign difference between the cosmological constant of the
Liouville gravity and that of the Einstein gravity. To argue for the robustness
of our prediction, we introduce the concept of time-dependent infrared
counter-terms and examine if they recover the de-Sitter invariance in the
$\lambda \phi^4$ theory in comparison with the Sine-Gordon model where it was
possible.

• Yu Nakayama

2014年11月4日

詳細を見る

When a globally supersymmetric theory is scale invariant, it must possess a
Virial supercurrent supermultiplet. The multiplet structure is analogous to the
R-current supermultiplet in globally R-symmetric theories but we put extra
"$i$"s in various formulae. We construct a novel type of supergravity from
gauging the Virial supercurrent supermultiplet in $d=1+3$ dimensions. We give
the full non-linear superspace action with the help of a covariantly linear
unitary superconformal compensator. The resulting supergravity is peculiar: (1)
no Einstein-like second order kinetic term is allowed without matter (2) there
exists a dynamical non-geometrical connection (3) the metric is unimodular in
the Wess-Zumino gauge and can be coupled only to scale invariant matter.
Examples of matter couplings and higher derivative kinetic terms are studied
from the superconformal approach. Our work completes the classification of the
irreducible $\mathcal{N}=1$ supergravities in $d=1+3$ dimensions.

• Yu Nakayama, Tomoki Ohtsuki

2014年7月23日

詳細を見る

In view of its physical importance in predicting the order of chiral phase
transitions in QCD and frustrated spin systems, we perform the conformal
bootstrap program of $O(n)\times O(2)$-symmetric conformal field theories in
$d=3$ dimensions with a special focus on $n=3$ and $4$. The existence of
renormalization group fixed points with these symmetries has been controversial
over years, but our conformal bootstrap program provides the non-perturbative
evidence. In both $n=3$ and $4$ cases, we find singular behaviors in the bounds
of scaling dimensions of operators in two different sectors, which we claim
correspond to chiral and collinear fixed points, respectively. In contrast to
the cases with larger values of $n$, we find no evidence for the anti-chiral
fixed point. Our results indicate the possibility that the chiral phase
transitions in QCD and frustrated spin systems are continuous with the critical
exponents that we predict from the conformal bootstrap program.

• Ariel Edery, Yu Nakayama

2014年5月31日

詳細を見る

We discuss the physics of {\it restricted Weyl invariance}, a symmetry of
dimensionless actions in four dimensional curved space time. When we study a
scalar field nonminimally coupled to gravity with Weyl(conformal) weight of
$-1$ (i.e. scalar field with the usual two-derivative kinetic term), we find
that dimensionless terms are either fully Weyl invariant or are Weyl invariant
if the conformal factor $\Omega(x)$ obeys the condition
$g^{\mu\nu}\nabla_{\mu}\nabla_{\nu}\Omega=0$. We refer to the latter as {\it
restricted Weyl invariance}. We show that all the dimensionless geometric terms
such as $R^2$, $R_{\mu\nu}R^{\mu\nu}$ and
$R_{\mu\nu\sigma\tau}R^{\mu\nu\sigma\tau}$ are restricted Weyl invariant.
Restricted Weyl transformations possesses nice mathematical properties such as
the existence of a composition and an inverse in four dimensional space-time.
We exemplify the distinction among rigid Weyl invariance, restricted Weyl
invariance and the full Weyl invariance in dimensionless actions constructed
out of scalar fields and vector fields with Weyl weight zero.

• Yu Nakayama, Tomoki Ohtsuki

2014年4月21日

詳細を見る

We investigate the conformal bootstrap approach to $O(N)$ symmetric CFTs in
five dimension with particular emphasis on the lower bound on the current
central charge. The bound has a local minimum for all $N>1$, and in the large
$N$ limit we propose that the minimum is saturated by the critical $O(N)$
vector model at the UV fixed point, the existence of which has been recently
argued by Fei, Giombi, and Klebanov. The location of the minimum is generically
different from the minimum of the lower bound of the energy-momentum tensor
central charge when it exists for smaller $N$.
To better understand the situation, we examine the lower bounds of the
current central charge of $O(N)$ symmetric CFTs in three dimension to compare.
We find the similar agreement in the large $N$ limit but the discrepancy for
smaller $N$ with the other sectors of the conformal bootstrap.

• Yu Nakayama, Tomoki Ohtsuki

2014年4月2日

詳細を見る

$O(n) \times O(m)$ symmetric Landau-Ginzburg models in $d=3$ dimension
possess a rich structure of the renormalization group and its understanding
offers a theoretical prediction of the phase diagram in frustrated spin models
with non-collinear order. Depending on $n$ and $m$, they may show
chiral/anti-chiral/Heisenberg/Gaussian fixed points within the same
universality class. We approach all the fixed points in the conformal bootstrap
program by examining the bound on the conformal dimensions for scalar operators
as well as non-conserved current operators with consistency crosschecks. For
large $n/m$, we show strong evidence for the existence of four fixed points by
comparing the operator spectrum obtained from the conformal bootstrap program
with that from the large $n/m$ analysis. We propose a novel non-perturbative
approach to the determination of the conformal window in these models based on
the conformal bootstrap program. From our numerical results, we predict that
for $m=3$, $n=7\sim 8$ is the edge of the conformal window for the anti-chiral
fixed points.

• Shinsuke Kawai, Yu Nakayama

2014年3月25日

詳細を見る

In holographic models of cosmology based on the (A)dS/CFT correspondence,
conformal symmetry is implicit in the dual description of the Universe.
Generically, however, one cannot expect the (broken) conformal invariance in
the cosmic fluctuations as only the scale invariance is manifest in
experiments. Also, in order for the prediction of the holographic models to
make sense, the conformal symmetry needs to be broken as the scalar mode of the
metric fluctuations becomes pure gauge in the conformal limit. We discuss the
improvement ambiguity of the energy-momentum tensor in this context and
construct a holographic model of the Universe that preserves the scale
invariance but not necessarily the full conformal invariance. Our sample
computation using a weakly coupled dual field theory shows that the orthogonal
type of non-Gaussianity is present over and above the equilateral type. The
improvement ambiguity corresponds to the choice of the energy momentum tensor
that will couple to our particle physics sector after inflation. Our results
show that the holographic prediction of the cosmological parameters crucially
depends on such a choice.

• Yu Nakayama

2014年1月21日

詳細を見る

We show that a "constructive derivation" of the AdS/CFT correspondence based
on the quantum local renormalization group in large N quantum field theories
consistently provides the a-c holographic Weyl anomaly in d=4 at the curvature
squared order in the bulk action. The consistency of the construction further
predicts the form of the metric beta function.

• K. -I. Ishikawa, Y. Iwasaki, Yu Nakayama, T. Yoshie

2013年10月18日

詳細を見る

We investigate SU(3) gauge theories in four dimensions with Nf fundamental
fermions, on a lattice using the Wilson fermion. Clarifying the vacuum
structure in terms of Polyakov loops in spatial directions and properties of
temporal propagators using a new method "local analysis", we conjecture that
the "conformal region" exists together with the confining region and the
deconfining region in the phase structure parametrized by beta and K, both in
the cases of the large Nf QCD within the conformal window (referred as
Conformal QCD) with an IR cutoff and small Nf QCD at T/Tc>1 with Tc being the
chiral transition temperature (referred as High Temperature QCD).
Our numerical simulation on a lattice of the size 16^3 x 64 shows the
following evidence of the conjecture. In the conformal region we find the
vacuum is the nontrivial Z(3) twisted vacuum modified by non-perturbative
effects and temporal propagators of meson behave at large t as a power-law
corrected Yukawa-type decaying form. The transition from the conformal region
to the deconfining region or the confining region is a sharp transition between
different vacua and therefore it suggests a first order transition both in
Conformal QCD and in High Temperature QCD.
Within our fixed lattice simulation, we find that there is a precise
correspondence between Conformal QCD and High Temperature QCD in the temporal
propagators under the change of the parameters Nf and T/Tc respectively. In
particular, we find the correspondence between Conformal QCD with Nf = 7 and
High Temperature QCD with Nf=2 at T ~ 2 Tc being in close relation to a meson
unparticle model. From this we estimate the anomalous mass dimension gamma* =
1.2 (1) for Nf=7. We also show that the asymptotic state in the limit T/Tc -->
infty is a free quark state in the Z(3) twisted vacuum.

• Yu Nakayama

2013年10月2日

詳細を見る

We propose various properties of renormalization group beta functions for
vector operators in relativistic quantum field theories. We argue that they
must satisfy compensated gauge invariance, orthogonality with respect to scalar
beta functions, Higgs-like relation among anomalous dimensions and a gradient
property. We further conjecture that non-renormalization holds if and only if
the vector operator is conserved. The local renormalization group analysis
guarantees the first three within power counting renormalization. We verify all
the conjectures in conformal perturbation theories and holography in the weakly
coupled gravity regime.

• Yu Nakayama

2013年7月30日

詳細を見る

We discuss Weyl anomaly and consistency conditions of local renormalization
group in d=1+2 dimensional quantum field theories. We give a classification of
the consistency conditions and ambiguities in most generality within the
power-counting renormalization scheme. They provide many non-trivial
constraints on possible forms of beta functions, anomalous dimensions and Weyl
anomaly of general d=1+2 dimensional quantum field theories. We perform modest
checks of our results in conformal perturbation theories, supersymmetric field
theories and holographic computations.

• Yu Nakayama

2013年5月17日

詳細を見る

We give a holographic explanation how the renormalization group approach to
singular perturbations in non-linear differential equations proposed by Chen,
Goldenfeld and Oono is indeed equivalent to a renormalization group method in
quantum field theories proposed by Gell-Mann and Low via AdS/CFT
correspondence.

• Yu Nakayama

2013年5月16日

詳細を見る

As an existence proof of the (0,2) heterotic supercurrent supermultiplets in
(1+1) dimensional quantum field theories which are consistent with the warped
superconformal algebra, we construct the (0,2) chiral Liouville field theories.
The two distinct possibilities of the heterotic supercurrent supermultiplets
are both realized.

• Yu Nakayama

2013年5月13日

詳細を見る

We present various (0,2) heterotic supercurrent supermultiplets in (1+1)
dimensional quantum field theories. From the minimal supercurrent
supermultiplets, we deduce conditions on symmetry enhancement such as Lorentz
invariance, (chiral) dilatation invariance, R-invariance, (chiral) conformal
invariance and their various combinations. Our construction covers many
interesting and/or exotic possibilities such as Lifshitz supersymmetry and
warped superconformal algebra. We also discuss the corresponding supergravity
by gauging the supercurrent supermultiplet. In particular, we propose a novel
class of heterotic supergravity based on the virial supercurrent.

• K. -I. Ishikawa, Y. Iwasaki, Yu Nakayama, T. Yoshie

2013年4月16日

詳細を見る

We give a new perspective on the properties of quarks and gluons at finite
temperature T in N_f = 2 ~ 6 QCD. We point out the existence of an IR fixed
point for the gauge coupling constant at T>T_c (T_c is the chiral phase
transition temperature). Based on this observation we predict theoretically and
verify numerically that the correlation functions of a meson G(t) at T/T_c > 1
decay with a power-law corrected Yukawa-type decaying form, G(t)=c exp(-m
t)/t^alpha in the "conformal region" defined by m < c Lambda_IR, where
Lambda_IR is the IR cutoff, m is the characteristic scale of the spectrum in
the meson cannel and c is a constant of order 1. The decaying form is the
characteristics of conformal theories with an IR cutoff. We discuss in detail
how the resulting hyper scaling relation of physical observables may modify the
existing argument about the order of the chiral phase transition in the N_f=2
case.

• Yu Nakayama

2013年2月4日

詳細を見る

In this review article, we discuss the distinction and possible equivalence
between scale invariance and conformal invariance in relativistic quantum field
theories. Under some technical assumptions, we can prove that scale invariant
quantum field theories in $d=2$ dimension necessarily possess the enhanced
conformal symmetry. The use of the conformal symmetry is well appreciated in
the literature, but the fact that all the scale invariant phenomena in $d=2$
dimension enjoy the conformal property relies on the deep structure of the
renormalization group. The outstanding question is whether this feature is
specific to $d=2$ dimension or it holds in higher dimensions, too. As of
January 2014, our consensus is that there is no known example of scale
invariant but non-conformal field theories in $d=4$ dimension under the
assumptions of (1) unitarity, (2) Poincar\'e invariance (causality), (3)
discrete spectrum in scaling dimension, (4) existence of scale current and (5)
unbroken scale invariance in the vacuum. We have a perturbative proof of the
enhancement of conformal invariance from scale invariance based on the higher
dimensional analogue of Zamolodchikov's $c$-theorem, but the non-perturbative
proof is yet to come. As a reference we have tried to collect as many
interesting examples of scale invariance in relativistic quantum field theories
as possible in this article. We give a complementary holographic argument based
on the energy-condition of the gravitational system and the space-time
diffeomorphism in order to support the claim of the symmetry enhancement. We
believe that the possible enhancement of conformal invariance from scale
invariance reveals the sublime nature of the renormalization group and
space-time with holography.

• K. -I. Ishikawa, Y. Iwasaki, Yu Nakayama, T. Yoshie

2013年1月21日

詳細を見る

We give a new perspective on the dynamics of conformal theories realized in
the SU(N) gauge theory, when the number of flavors N_f is within the conformal
window. Motivated by the RG argument on conformal theories with a finite IR
cutoff \Lambda_{IR}, we conjecture that the propagator of a meson G_H(t) on a
lattice behaves at large t as a power-law corrected Yukawa-type decaying form
G_H(t) = c_H \exp{(-m_H t)}/t^{\alpha_H} instead of the exponentially decaying
form c_H\exp{(-m_H t)}, in the small quark mass region where m_H \le c
\Lambda_{IR}: m_H is the mass of the ground state hadron in the channel H and c
is a constant of order 1. The transition between the "conformal region" and the
"confining region" is a first order transition. Our numerical results verify
the predictions for the N_f=7 case and the N_f=16 case in the SU(3) gauge
theory with the fundamental representation.

• Yu Nakayama

2012年11月19日

詳細を見る

Null energy condition plays a crucial role in holographic renormalization
group flow, leading to the holographic c-theorem. Unfortunately, the null
energy condition is quantum mechanically violated. Even the averaged version
can be violated. We discuss how the anomalous violation of the null energy
condition affects the holographic renormalization group flow in 1+3 dimensional
bulk gravity. We show that despite the violation of the null energy condition,
a suitably modified holographic c-function with a peculiar log correction is
still monotonically decreasing in so far as we add the counterterm that removes
a ghost mode of gravity.

• Yu Nakayama

2012年10月24日

詳細を見る

We discuss boundary conditions for conformal field theories that preserve the
boundary Poincare invariance. As in the bulk field theories, a question arises
whether boundary scale invariance leads to boundary conformal invariance. With
unitarity, Cardy's condition of vanishing momentum flow is necessary for the
boundary conformal invariance, but it is not sufficient in general. We show
both a proof and a counterexample of the enhancement of boundary conformal
invariance in (1+1) dimension, which depends on the extra assumption we make.
In (1+2) dimension, Cardy's condition is shown to be sufficient. In higher
dimensions, we give a perturbative argument in favor of the enhancement based
on the boundary g-theorem. With the help of the holographic dual recently
proposed, we show a holographic proof of the boundary conformal invariance
under the assumption of the boundary strict null energy condition, which also
gives a sufficient condition for the strong boundary g-theorem.

• Yu Nakayama

2012年8月23日

詳細を見る

Supersymmetric field theories possess a rich structure in their supercurrent
supermultiplets. Some symmetries are manifest in one supercurrent
supermultiplet but not in the others; for instance, R-symmetry is manifest in
the R-multiplet but not in the Ferrara-Zumino multiplet. Similarly, we argue
that dilatation symmetry is manifest in the Virial multiplet (also known as a
variant minimal supercurrent supermultiplet in the literature). It reveals that
R-symmetry and dilatation symmetry are conceptually independent without further
assumptions even though the superconformal symmetry connects the two. We show
the structure of the Virial multiplet for general renormalizable supersymmetric
field theories in (1+3) dimension to all orders in perturbation theory, and
discuss the condition for the dilatation invariance (but not necessarily
R-symmetric nor superconformal). We present novel scale invariant trajectories
with a nilpotent structure in coupling constants for non-unitary Wess-Zumino
models with non-vanishing beta functions, which are, therefore, not
superconformal.

• Yu Nakayama

2012年6月12日

詳細を見る

We show that relativistic hydrodynamics in Minkowski space-time has intrinsic
ambiguity in second order viscosity parameters in the Landau-Lifshitz frame.
This stems from the possibility of improvements of energy-momentum tensor.
There exist at least two viscosity parameters which can be removed by using
this ambiguity in scale invariant hydrodynamics in (1+3) dimension, and
seemingly non-conformal hydrodynamic theories can be hiddenly conformal
invariant.

• Yu Nakayama

2012年3月5日

詳細を見る

From the holographic renormalizationg group viewpoint, while the scale
transformation plays a primary role in the duality by providing the extra
dimension, the special conformal transformation seems to only play a secondary
role. We, however, claim that the space-time diffeomorphism is crucially
related to the latter. For its demonstration, we study the holographic
renormalization group flow of a foliation preserving diffeomophic theory of
gravity (a.k.a. space-time flipped Horava gravity). We find that the dual field
theory, if any, is only scale invariant but not conformal invariant. In
particular, we show that the holographic trace anomaly in four-dimension
predicts the Ricci scalar squared term that would be incompatible with the
Wess-Zumino consistency condition if it were conformal. This illustrates how
the foliation preserving diffeomophic theory of gravity could be inconsistent
with a theorem of the dual unitary quantum field theory.

• Yu Nakayama

2012年1月17日

詳細を見る

It is logically possible that the trace anomaly in four dimension includes
the Hirzebruch-Pontryagin density in CP violating theories. Although the term
vanishes at free conformal fixed points, we realize such a possibility in the
holographic renormalization group and show that it is indeed possible. The
Hirzebruch-Pontryagin term in the trace anomaly may serve as a barometer to
understand how much CP is violated in conformal field theories.

• Yu Nakayama

2011年12月3日

詳細を見る

We provide a gravity counterpart of the theorem by Hofman and Strominger that
in (1+1) dimension, chiral scale invariance indicates chiral conformal
invariance. We show that the strict null energy condition gives a sufficient
condition to guarantee the symmetry enhancement. We also investigate a
possibility to construct holographic c-function that decreases along the
holographic renormalization group flow.

• Yu Nakayama

2011年10月12日

詳細を見る

The derivation of the a-theorem recently proposed by Komargodski and
Schwimmer relies on the \epsilon-conjecture that demands decoupling of dilaton
from the rest of the infrared theory. We point out that the decoupling, if
true, provides a strong evidence for the equivalence between scale invariance
and conformal invariance in four dimension. Thus, a complete proof of the
a-theorem along the line of their argument in the most generic scenario would
establish the equivalence between scale invariance and conformal invariance,
which is another long-standing conjecture in four-dimensional quantum field
theories.

• Yu Nakayama

2011年9月27日

詳細を見る

We investigate a possibility of scale invariant but non-conformal
supersymmetric field theories from a perturbative approach. The explicit
existence of monotonically decreasing a-function that generates beta-functions
as a gradient flow provides a strong obstruction for such a possibility at
two-loop order. We comment on the "discovery" of scale invariant but
non-conformal renormalization group trajectories via a "change of scheme" in
(4-\epsilon) dimension proposed in literatures.

• Yu Nakayama

2011年7月14日

詳細を見る

We construct a gravity dual for scale invariant but non-conformal field
theories with a cyclic renormalization group flow. A slight modification of our
construction gives a gravity dual of discretely scale invariant field theories.
The underlying gravitational theory breaks the null energy condition.

• Yu Nakayama, Hirosi Ooguri

2011年6月27日

詳細を見る

Nekrasov's partition function is defined on a flat bundle of R^4 over S^1
called the Omega background. When the fibration is self-dual, the partition
function is known to be equal to the topological string partition function,
which computes scattering amplitudes of self-dual gravitons and graviphotons in
type II superstring compactified on a Calabi-Yau manifold. We propose a
generalization of this correspondence when the fibration is not necessarily
self-dual.

• Yu Nakayama

2011年5月24日

詳細を見る

We study the superconformal index of the N=4 super-Yang-Milles theory on S^3
X S^1 with the half BPS superconformal surface operator (defect) inserted at
the great circle of S^3. The half BPS superconformal surface operators preserve
the same supersymmetry as well as the symmetry of the chemical potential used
in the definition of the superconformal index, so the structure and the
parameterization of the superconformal index remain unaffected by the presence
of the surface operator. On the surface defect, a two-dimensional (4,4)
superconformal field theory resides, and the four-dimensional superconformal
index may be regarded as a superconformal index of the two-dimensional (4,4)
superconformal field theory coupled with the four-dimensional bulk system. We
construct the matrix model that computes the superconformal index with the
surface operator when it couples with the bulk N=4 super-Yang-Milles theory
through the defect hypermultiplets on it.

• Sheer El-Showk, Yu Nakayama, Slava Rychkov

2011年1月27日

詳細を見る

The free Maxwell theory in D<>4 dimensions provides a physical example of a
unitary, scale invariant theory which is NOT conformally invariant. The easiest
way to see this is that the field strength operator F_mn is neither a primary
nor a descendant. We show how conformal multiplets can be completed, and
conformality restored, by adding new local operators to the theory. In D>=5,
this can only be done by sacrificing unitarity of the extended Hilbert space.
We analyze the full symmetry structure of the extended theory, which turns out
to be related to the OSp(D,2|2) superalgebra.

• Yu Nakayama

2010年9月2日

詳細を見る

We study the implication of refined topological string amplitudes in the
supersymmetric N=1 flux compactification. They generate higher derivative
couplings among the vector multiplets and graviphoton with generically
non-holomorphic moduli dependence. For a particular term, we can compute them
by assuming the geometric engineering. We claim that the Dijkgraaf-Vafa large N
matrix model with the beta-ensemble measure directly computes the higher
derivative corrections to the supersymmetric effective action of the
supersymmetric N=1$gauge theory. • Yu Nakayama 2010年9月2日 詳細を見る We study higher derivative corrections in holographic dual of Zamolodchikov-Polchinski theorem that states the equivalence between scale invariance and conformal invariance in unitary d-dimensional Poincare invariant field theories. From the dual holographic perspective, we find that a sufficient condition to show the holographic theorem is the generalized strict null energy condition of the matter sector in effective (d+1)-dimensional gravitational theory. The same condition has appeared in the holographic dual of the "c-theorem" and our theorem suggests a deep connection between the two, which was manifested in two-dimensional field theoretic proof of the both. • Yu Nakayama 2010年7月30日 詳細を見る We present a concrete holographic realization of the eternal inflation and its census taker in (1+1) dimensional Liouville gravity by applying the FRW/CFT philosophy proposed by Freivogel, Sekino, Susskind and Yeh (FSSY). The dual boundary theory is nothing but the old matrix model describing the two-dimensional Liouville gravity coupled with minimal model matter fields. In Liouville gravity, the flat Minkowski space or even the AdS space will decay into the dS space, which is in stark contrast with higher dimensional theories, but the spirit of the FSSY conjecture applies with only minimal modification. We investigate the classical geometry as well as some correlation functions to support our claim. We also study an analytic continuation to the time-like Liouville theory to discuss possible applications in (1+3) dimensional cosmology along with the original FSSY conjecture, where the boundary theory involves the time-like Liouville theory. We show that the decay rate in the (1+3) dimension is more suppressed due to the quantum gravity correction of the boundary theory. • Yu Nakayama 2010年4月17日 詳細を見る Antoniadis et al proposed a relation between the Omega-deformation and refined correlation functions of the topological string theory. We investigate the proposal for the deformed conifold geometry from a non-compact Gepner model approach. The topological string theory on the deformed conifold has a dual description in terms of the c=1 non-critical string theory at the self-dual radius, and the Omega-deformation yields the radius deformation. We show that the refined correlation functions computed from the twisted SL(2,R)/U(1) Kazama-Suzuki coset model at level k=1 have direct c=1 non-critical string theory interpretations. After subtracting the leading singularity to procure the 1PI effective action, we obtain the agreement with the proposal. • Yu Nakayama 2010年3月30日 詳細を見る One of the salient features of human perception is its invariance under dilatation in addition to the Euclidean group, but its non-invariance under special conformal transformation. We investigate a holographic approach to the information processing in image discrimination with this feature. We claim that a strongly coupled analogue of the statistical model proposed by Bialek and Zee can be holographically realized in scale invariant but non-conformal Euclidean geometries. We identify the Bayesian probability distribution of our generalized Bialek-Zee model with the GKPW partition function of the dual gravitational system. We provide a concrete example of the geometric configuration based on a vector condensation model coupled with the Euclidean Einstein-Hilbert action. From the proposed geometry, we study sample correlation functions to compute the Bayesian probability distribution. • Yu Nakayama 2010年2月3日 詳細を見る We investigate universal time-dependent exact deformations of Schrodinger geometry. We present 1) scale invariant but non-conformal deformation, 2) non-conformal but scale invariant deformation, and 3) both scale and conformal invariant deformation. All these solutions are universal in the sense that we could embed them in any supergravity constructions of the Schrodinger invariant geometry. We give a field theory interpretation of our time-dependent solutions. In particular, we argue that any time-dependent chemical potential can be treated exactly in our gravity dual approach. • Yu Nakayama 2010年1月20日 詳細を見る We investigate possibilities for a Schr\"odinger-like gravity with the dynamical critical exponent$z=2$, where the action only contains the first-order time derivative. The Horava gravity always admits such a relevant deformation because the full$(d+1)$dimensional diffeomorphism of the Einstein gravity is replaced by the foliation preserving diffeomorphism. The dynamics is locally trivial or topological in the pure gravity case, but we can construct a dynamical field theory with a$z=2$dispersion relation by introducing a dilaton degree of freedom. Our model provides a classical starting point for the possible quantum dilaton gravity which may be applied to a membrane quantization. • Scale invariance vs conformal invariance from holography 査読有り Yu Nakayama Int.J.Mod.Phys.A 2010年 詳細を見る 記述言語：英語 掲載種別：研究論文（学術雑誌） • Yu Nakayama 2009年12月28日 詳細を見る We study a possibility of anisotropic scale invariant cosmology. It is shown that within the conventional Einstein gravity, the violation of the null energy condition is necessary. We construct an example based on a ghost condensation model that violates the null energy condition. The cosmological solution necessarily contains at least one contracting spatial direction as in the Kasner solution. Our cosmology is conjectured to be dual to, if any, a non-unitary anisotropic scale invariant Euclidean field theory. We investigate simple correlation functions of the dual theory by using the holographic computation. After compactification of the contracting direction, our setup may yield a dual field theory description of the winding tachyon condensation that might solve the singularity of big bang/crunch of the universe. • Yu Nakayama 2009年9月24日 詳細を見る Scale invariant but non-conformal field theories are forbidden in (1+1) dimension, and so should be the corresponding holographic dual gravity theories. We conjecture that such scale invariant but non-conformal field configurations do not exist in the string/M-theory. We provide a proof of this conjecture in the classical supergravity limit under a certain gauge condition. Our proof does also apply in higher dimensional scale invariant but non-conformal field configurations, which suggests that scale invariant but non-conformal field theories may be forbidden in higher dimensions as well. • Yu Nakayama 2009年7月1日 詳細を見る We present a class of field configurations that are forbidden in the quantum gravity because of inconsistency in the dual field theory from holography. Scale invariant but non-conformal field theories are impossible in (1+1) dimension, and so should be the corresponding gravity dual. In particular, the "spontaneous Lorentz symmetry breaking" models and the "ghost condensation" models, which are well-studied in phenomenology literatures, are forbidden in any consistent quantum theories of gravity in (1+2) dimension since they predict such inconsistent field configurations. • Yu Nakayama 2009年6月23日 詳細を見る We study scale invariant but not necessarily conformal invariant deformations of non-relativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a massive vector field. We find that, within the class of metric we study, when we assume the Galilean invariance, the scale invariant deformation always preserves the non-relativistic conformal invariance. We discuss applications to scaling regime of Reggeon field theory and non-linear quantum finance. These theories possess scale invariance but may or may not break the conformal invariance, depending on the underlying symmetry assumptions. • Heng-Yu Chen, Yu Nakayama, Gary Shiu 2009年5月27日 詳細を見る We study the dynamics of a D3 brane in generic IIB warped compactifications, using the Hamiltonian formulation discussed in arXiv:0805.3700 [hep-th]. Taking into account of both closed and open string fluctuations, we derive the warped Kahler potential governing the motion of a probe D3 brane. By including the backreaction of D3, we also comment on how the problem of defining a holomorphic gauge coupling on wrapped D7 branes in warped background can be resolved. • Yu Nakayama, Soo-Jong Rey 2009年5月18日 詳細を見る Non-relativistic ABJM theory is defined by Galilean limit of mass-deformed N=6 Chern-Simons theory. Holographic string theory dual to the theory is not known yet. To understand features candidate gravity dual might exhibit, we examine local and nonlocal physical observables and their correlations in the non-relativistic ABJM theory. We show that gauge invariant local observables correspond to zero-norm states and that correlation functions among them are trivial. We also show that a particular class of nonlocal observables, Wilson loops, are topological in the sense that their correlation functions coincide with those of pure Chern-Simons theory. We argue that the theory is nevertheless physical and illustrate several physical observables whose correlation functions are nontrivial. We also study quantum aspects. We show that Chern-Simons level is finitely renormalized and that dilatation operator acting on spin chain is trivial at planar limit. These results all point to string scale geometry of gravity dual and to intriguing topological and tensionless nature of dual string defined on it. • Chiu Man Ho, Yu Nakayama 2009年3月3日 詳細を見る We revisit the unparticle interactions and propagators from the AdS-CFT point of view, and we show how the contact terms and their renormalization group flow appear in the context of the holographic renormalization. We study both vector unparticles and unfermions, uncovering the relevant boundary conditions and renormalization group flows. • Masahiro Ibe, Yu Nakayama, Hitoshi Murayama, Tsutomu T. Yanagida 2009年2月17日 詳細を見る We propose a model of dark matter identified with a pseudo-Nambu-Goldstone boson in the dynamical supersymmetry breaking sector in a gauge mediation scenario. The dark matter particles annihilate via a below-threshold narrow resonance into a pair of R-axions each of which subsequently decays into a pair of light leptons. The Breit-Wigner enhancement explains the excess electron and positron fluxes reported in the recent cosmic ray experiments PAMELA, ATIC and PPB-BETS without postulating an overdensity in halo, and the limit on anti-proton flux from PAMELA is naturally evaded. • Yu Nakayama 2009年2月13日 詳細を見る We construct a superfield formulation for non-relativistic Chern-Simons-Matter theories with manifest dynamical supersymmetry. By eliminating all the auxiliary fields, we show that the simple action reduces to the one obtained by taking non-relativistic limit from the relativistic Chern-Simons-Matter theory proposed in the literature. As a further application, we give a manifestly supersymmetric derivation of the non-relativistic ABJM theory. • Yu Nakayama, Makoto Sakaguchi, Kentaroh Yoshida 2009年2月12日 詳細を見る We study non-relativistic limits of the N=6 Chern-Simons-Matter theory that arises as a low-energy limit of the M2-brane gauge theory with background flux. The model admits several different non-relativistic limits and we find that the maximal supersymmetry we construct has 14 components of supercharges, which is a novel example of non-relativistic superconformal algebra in (1+2) dimension. We also investigate the other limits that realize less supersymmetries. • Conformal Gauge Mediation and Light Gravitino of Mass m(3/2) < O(10) eV 査読有り Masahiro Ibe, Yu Nakayama, Tsutomu Yanagida Phys.Lett.B 2009年 詳細を見る 記述言語：英語 掲載種別：研究論文（学術雑誌） • Yu Nakayama 2008年12月11日 詳細を見る We investigate the near-horizon limit of extremally rotating NS5-branes. The resulting geometry has SL(2,R) \times U(1)^2 isometry. The asymptotic symmetry group contains a chiral Virasoro algebra, and we obtain two different realizations depending on the boundary conditions we impose. When one of the two angular momenta vanishes, the symmetry is enhanced to AdS_3. The entropy of the boundary theory can be estimated from the Cardy formula and it agrees with the Bekenstein-Hawking entropy of the bulk theory. We can embed the extremally rotating NS5-brane geometry in an exactly solvable string background, which may yield microscopic understanding of this duality, especially about the mysterious enhancement of the symmetry from AdS_2 to AdS_3. The construction suggests emerging Virasoro symmetries in the extreme corner of the (1+5) dimensional little string theory. • Yu Nakayama, Makoto Sakaguchi, Kentaroh Yoshida 2008年12月8日 詳細を見る We construct an example of supersymmetric Chern-Simons-matter theory with a matter field transforming as a singlet representation of the supersymmetry algebra, where the bosonic and fermionic degrees of freedom do not match. This is obtained as a non-relativistic limit of the N=2 Chern-Simons-matter theory in 1+2 dimensions, where the particle and anti-particle coexist. We also study the index to investigate the mimatch of bosonic and fermionic degrees of freedom. • Yu Nakayama, Shinsei Ryu, Makoto Sakaguchi, Kentaroh Yoshida 2008年11月15日 詳細を見る We investigate non-relativistic limits of the N=3 Chern-Simons matter system in 1+2 dimensions. The relativistic theory can generate several inequivalent super Schodinger invariant theories, depending on the degrees of freedom we choose to retain in the non-relativistic limit. The maximally supersymmetric Schrodinger invariant theory is obtained by keeping all particle degrees of freedom. The other descendants, where particles and anti-particles coexist, are also Schrodinger invariant but preserve less supersymmetries. Thus, we have a family of super Schrodinger invariant field theories produced from the parent relativistic theory. • Yu Nakayama 2008年10月22日 詳細を見る We study (0,2) deformations of N=2 Liouville field theory and its mirror duality. A gauged linear sigma model construction of the ultraviolet theory connects (0,2) deformations of Liouville field theory and (0,2) deformations of N=2 SL(2,R)/U(1) coset model as a mirror duality. Our duality proposal from the gauged linear sigma model completely agrees with the exact CFT analysis. In the context of heterotic string compactifications, the deformation corresponds to the introduction of a non-trivial gauge bundle. This non-compact Landau-Ginzburg construction yields a novel way to study the gauge bundle moduli for non-compact Calabi-Yau manifolds. • Yu Nakayama 2008年7月21日 詳細を見る We study the highest-weight representation of N=2 supersymmetric Schrodinger algebra which appears in non-relativistic superconformal field theories in (1+2) dimension. We define the index for the non-relativistic superconformal field theories and study its properties. As a concrete example, we compute the index for the non-relativistic limit of N=6 superconformal Chern-Simons-matter theory recently proposed by Aharony et al. • Gaston Giribet, Yu Nakayama, Lorena Nicolas 2008年5月9日 詳細を見る We show a physical realization of the Langlands duality in correlation functions of H_3^+ WZNW model. We derive a dual version of the Stoyanovky-Riabult-Teschner (SRT) formula that relates the correlation function of the H_3^+ WZNW and the dual Liouville theory to investigate the level duality k-2 \to (k-2)^{-1} in the WZNW correlation functions. Then, we show that such a dual version of the H_3^+ - Liouville relation can be interpreted as a particular case of a biparametric family of non-rational CFTs based on the Liouville correlation functions, which was recently proposed by Ribault. We study symmetries of these new non-rational CFTs and compute correlation functions explicitly by using the free field realization to see how a generalized Langlands duality manifests itself in this framework. Finally, we suggest an interpretation of the SRT formula as realizing the Drinfeld-Sokolov Hamiltonian reduction. Again, the Hamiltonian reduction reveals the Langlands duality in the H_3^+ WZNW model. Our new identity for the correlation functions of H_3^+ WZNW model may yield a first step to understand quantum geometric Langlands correspondence yet to be formulated mathematically. • Chiu Man Ho, Yu Nakayama 2008年4月23日 詳細を見る We give a non-trivially interacting field theory example of scale invariant but non-conformal field theory. The model is based on the exactly solvable Liouville field theory coupled with free scalars deformed by an exactly marginal operator. We show non-vanishing of the trace of the energy-momentum tensor by using the quantum Schwinger-Dyson equation for the Liouville field theory, which is a sophistication of the quantum higher equations of motion for the Liouville field theory introduced by Alyosha Zamolodchikov. Possibly dangerous implications for the super-critical string theory will be discussed. • Conformal Supersymmetry Breaking and Dynamical Tuning of the Cosmological Constant 査読有り Masahiro Ibe, Yu Nakayama, Tsutomu Yanagida Phys.Lett.B 2008年 詳細を見る 記述言語：英語 掲載種別：研究論文（学術雑誌） • Yu Nakayama 2007年12月4日 詳細を見る We show a calculable example of stable supersymmetry (SUSY) breaking models with O(10) eV gravitino mass based on the combination of D-term gauge mediation and U(1)' mediation. A potential problem of the negative mass squared for the SUSY standard model (SSM) sfermions in the D-term gauge mediation is solved by the contribution from the U(1)' mediation. On the other hand, the splitting between the SSM gauginos and sfermions in the U(1)' mediation is circumvented by the contributions from the D-term gauge mediation. Since the U(1)' mediation does not introduce any new SUSY vacua, we achieve a completely stable model under thermal effects. Our model, therefore, has no cosmological difficulty. • Yu Nakayama, Masahito Yamazaki, T. T. Yanagida 2007年9月28日 詳細を見る We present a stringy realization of the ISS metastable SUSY breaking model with moduli stabilization. The mass moduli of the ISS model is stabilized by gauging of a U(1) symmetry and its D-term potential. The SUSY is broken both by F-terms and D-terms. It is possible to obtain de-Sitter vacua with a vanishingly small cosmological constant by an appropriate fine-tuning of flux parameters. • Yu Nakayama 2007年7月17日 詳細を見る We investigate unparticle physics with supersymmetry (SUSY). The SUSY breaking effects due to the gravity mediation induce soft masses for the SUSY unparticles and hence break the conformal invariance. The unparticle physics observable in near future experiments is only consistent if the SUSY breaking effects from the hidden sector to the standard model sector are dominated by the gauge mediation, or if the SUSY breaking effects to the unparticle sector is sufficiently sequestered. We argue that the natural realization of the latter possibility is the conformal sequestering scenario. • Yu Nakayama 2007年6月6日 詳細を見る We further investigate the dimensional duality (D-duality) proposed in arXiv:0705.0550 by mainly focusing on the properties of D-branes in this background. We derive the world-sheet correspondence of static D-branes, and discuss the fate of non-static D-branes from the world-sheet viewpoint. The quantum string production with or without D-branes is also studied from the time-like Liouville theory. We find that the closed string production from the background is much larger than that from D-branes decaying into nothing. • Y. Nakayama, Masato Taki, Taizan Watari, T. T. Yanagida 2007年5月7日 詳細を見る We construct a gauge-mediation model with a D-term supersymmetry (SUSY) breaking. R-symmetry breaking necessary for generating the SUSY standard-model gaugino masses is given by gaugino condensation of a strongly coupled gauge theory in the hidden sector. The energy scale of the strong dynamics of the hidden sector gauge theory should be around the messenger mass scale M, or otherwise perturbative calculations would be reliable and would lead to negative soft mass squared for squarks and sleptons. Thus, all the mass scales are controlled by a virtually single parameter, \sqrt{D}/M. This model covers a very wide range of gravitino mass, m_{3/2} \simeq 1 eV--100 TeV. Possible embeddings of the model in string theory are also discussed. • M. Ibe, Y. Nakayama, T. T. Yanagida 2007年3月10日 詳細を見る We propose a one-parameter theory for gauge mediation of supersymmetry (SUSY) breaking. The spectrum of SUSY particles such as squarks and sleptons in the SUSY standard-model and the dynamics of SUSY-breaking sector are, in principle, determined only by one parameter in the theory, that is, the mass of messengers. Above the messenger threshold all gauge coupling and Yukawa coupling constants in the SUSY-breaking sector are on the infrared fixed point. We find that the present theory may predict a split spectrum of the standard-model SUSY particles, m_{gaugino} < m_{sfermion}, where m_{gaugino} and m_{sfermion} are SUSY-breaking masses for gauginos and squarks/sleptons, respectively. • Yu Nakayama 2007年2月28日 詳細を見る We investigate the black hole - string transition in the two-dimensional Lorentzian black hole system from the exact boundary states that describe the rolling D-brane falling down into the two-dimensional black hole. The black hole - string phase transition is one of the fundamental properties of the non-supersymmetric black holes in string theory, and we will reveal the nature of the phase transition from the exactly solvable world-sheet conformal field theory viewpoint. Since the two-dimensional Lorentzian black hole system (SL(2;R)_k/U(1) coset model at level k) typically appears as near-horizon geometries of various singularities such as NS5-branes in string theory, our results can be regarded as the probe of such singularities from the non-supersymmetric probe rolling D-brane. The exact construction of boundary states for the rolling D0-brane falling down into the two-dimensional D-brane enables us to probe the phase transition at k=1 directly in the physical amplitudes. During the study, we uncover three fundamental questions in string theory as a consistent theory of quantum gravity: small charge limit v.s. large charge limit of non-supersymmetric quantum black holes, analyticity v.s. non-analyticity in physical amplitudes and physical observables, and unitarity v.s. open closed duality in time-dependent string backgrounds. This work is based on the PhD thesis submitted to Department of Physics, Faculty of Science, University of Tokyo, which was defended on January 2007. • Yu Nakayama 2007年1月23日 詳細を見る We exactly compute the finite N index and BPS partition functions for N=4 SYM theory in a newly proposed maximal angular momentum limit. The new limit is not predicted from the superconformal algebra, but naturally arises from the supergravity dual. We show that the index does not receive any finite N corrections while the free BPS partition function does. • Yu Nakayama, Soo-Jong Rey, Yuji Sugawara 2006年6月14日 詳細を見る We propose a new worldsheet approach to the McGreevy-Silverstein proposal: resolution of spacelike singularity via Scherk-Schwarz compactification and winding string condensation therein. Our proposal is built upon so-called three parameter sine-Liouville theory, which has useful features and could be solvable in conformal field theory method. Utilizing standard Wick rotation, we compute string pair production rate exactly in terms of renormalized worldsheet cosmological constant and find that the production rate is finite for six or less spacetime dimensions. We also find that the sine-Liouville potential excises string excitation in the asymptotic past, and that such "Nothing state" is realizable for a range of sine-Liouville coupling constants. We compute one loop vacuum-to-vacuum transition amplitude and again detect presence of the "Nothing state". We also survey various worldsheet approaches to the tachyon condensation based on timelike Liouville theory. We point out that string theory on a conifold provides the upper critical dimension for realizing the "Nothing state", thus making contact with the blackhole / string transition point. • Yu Nakayama, Soo-Jong Rey, Yuji Sugawara 2006年5月1日 詳細を見る Investigations for decay of unstable D-brane and rolling of accelerated D-brane dynamics have revealed that various proposed prescriptions give different result for spectral amplitudes and observables. Here, we study them with particular attention to unitarity and open-closed channel duality. From "ab initio" derivation in the open string channel, both in Euclidean and Lorentzian worldsheet approaches, we find heretofore overlooked contribution to the spectral amplitudes and obervables. The contribution is fortuitously absent for decay of unstable D-brane, but is present for rolling of accelerated D-brane. We finally show that the contribution is imperative for ensuring unitarity and optical theorem at each order in string loop expansion. • Yu Nakayama 2006年2月28日 詳細を見る We compute the index for the conifold gauge theory from type IIB supergravity (superstring) on AdS_5 \times T^{1,1}. We discuss its implication from the gauge theory viewpoint. • Yu Nakayama 2005年12月22日 詳細を見る We compute the index for orbifold quiver gauge theories. We compare it with the results obtained from the type IIB supergravity (superstring) on AdS_5 \times S^5/\Gamma. • M. Ibe, K. -I. Izawa, Yu Nakayama, Y. Shinbara, T. Yanagida 2005年9月22日 詳細を見る We extend our models for conformal sequestering of dynamical supersymmetry breaking with decoupling vector-like matter in several different ways. These extensions enable us to simplify concrete model building, in particular, rendering large gauge group and ad hoc global symmetry for sequestering unnecessary. Conformal sequestering appears highly natural in such circumstances. • Yu Nakayama, Soo-Jong Rey, Yuji Sugawara 2005年7月5日 詳細を見る We study propagation of D0-brane in two-dimensional Lorentzian black hole backgrounds by the method of boundary conformal field theory of SL(2,R)/U(1) supercoset at level k. Typically, such backgrounds arise as near-horizon geometries of k coincident non-extremal NS5-branes, where 1/k measures curvature of the backgrounds in string unit and hence size of string worldsheet effects. At classical level, string worldsheet effects are suppressed and D0-brane propagation in the Lorentzian black hole geometry is simply given by the Wick rotation of D1-brane contour in the Euclidean black hole geometry. Taking account of string worldsheet effects, boundary state of the Lorentzian D0-brane is formally constructible via Wick rotation from that of the Euclidean D1-brane. However, the construction is subject to ambiguities in boundary conditions. We propose exact boundary states describing the D0-brane, and clarify physical interpretations of various boundary states constructed from different boundary conditions. As it falls into the black hole, the D0-brane radiates off to the horizon and to the infinity. From the boundary states constructed, we compute physical observables of such radiative process. We find that part of the radiation to infinity is in effective thermal distribution at the Hawking temperature. We also find that part of the radiation to horizon is in the Hagedorn distribution, dominated by massive, highly non-relativistic closed string states, much like the tachyon matter. Remarkably, such distribution emerges only after string worldsheet effects are taken exactly into account. From these results, we observe that nature of the radiation distribution changes dramatically across the conifold geometry k=1 (k=3 for the bosonic case), exposing the string - black hole transition' therein. • M. Ibe, K. -I. Izawa, Yu Nakayama, Y. Shinbara, T. Yanagida 2005年6月3日 詳細を見る We provide, in a framework of vector-like gauge theories, concrete models for conformal sequestering of dynamical supersymmetry (SUSY) breaking in the hidden sector. If the sequestering is sufficiently strong, anomaly mediation of the SUSY breaking may give dominant contributions to the mass spectrum of SUSY standard-model particles, leading to negative slepton masses squared. Thus, we also consider a model with gravitational gauge mediation to circumvent the tachyonic slepton problem in pure anomaly mediation models. • Gaston Giribet, Yu Nakayama 2005年5月23日 詳細を見る Recently, Ribault and Teschner pointed out the existence of a one-to-one correspondence between N-point correlation functions for the SL(2,C)_k/SU(2) WZNW model on the sphere and certain set of 2N-2-point correlation functions in Liouville field theory. This result is based on a seminal work by Stoyanovsky. Here, we discuss the implications of this correspondence focusing on its application to string theory on curved backgrounds. For instance, we analyze how the divergences corresponding to worldsheet instantons in AdS_3 can be understood as arising from the insertion of the dual screening operator in the Liouville theory side. We also study the pole structure of N-point functions in the 2D Euclidean black hole and its holographic meaning in terms of the Little String Theory. This enables us to interpret the correspondence between CFTs as encoding a LSZ-type reduction procedure. Furthermore, we discuss the scattering amplitudes violating the winding number conservation in those backgrounds and provide a formula connecting such amplitudes with observables in Liouville field theory. Finally, we study the WZNW correlation functions in the limit k -> 0 and show that, at the point k=0, the Stoyanovsky-Ribault-Teschner dictionary turns out to be in agreement with the FZZ conjecture at a particular point of the space of parameters where the Liouville central charge becomes c=-2. This result makes contact with recent studies on the dynamical tachyon condensation in closed string theory. • Yu Nakayama, Kamal L. Panigrahi, Soo-Jong Rey, Hiromitsu Takayanagi 2004年12月5日 詳細を見る We study rolling radion dynamics of electrified D-brane in NS5-brane background, both in effective field theory and in full open string theory. We construct exact boundary states and, from them, extract conserved Noether currents. We argue that T-duality and Lorentz boost offer an intuitive approach. In the limit of large number of NS5-branes, both boundary wave functions and conserved currents are sharply peaked and agree with those deduced from the effective field theory. As the number of NS5-branes is reduced, width around the peak becomes wider by string corrections. We also study radiative decay process. By applying Lorentz covariance, we show how the decay of electrified D-brane is related to that of bare D-brane. We compute spectral moments of final state energy and winding quantum number. Using Lorentz covariance argument, we explain in elementary way why winding quantum number should be included and derive rules how to do so. We conclude that Kutasov's "geometric realization" between radion rolling dynamics and tachyon rolling dynamics holds universally, both for bare and electrified D-branes. • Gaetano Bertoldi, Stefano Bolognesi, Gaston Giribet, Marco Matone, Yu Nakayama 2004年9月22日 詳細を見る We study the connection between Zamolodchikov operator-valued relations in Liouville field theory and in the SL(2,R)_k WZNW model. In particular, the classical relations in SL(2,R)_k can be formulated as a classical Liouville hierarchy in terms of the isotopic coordinates, and their covariance is easily understood in the framework of the AdS_3/CFT_2 correspondence. Conversely, we find a closed expression for the classical Liouville decoupling operators in terms of the so called uniformizing Schwarzian operators and show that the associated uniformizing parameter plays the same role as the isotopic coordinates in SL(2,R)_k. The solutions of the j-th classical decoupling equation in the WZNW model span a spin j reducible representation of SL(2,R). Likewise, we show that in Liouville theory solutions of the classical decoupling equations span spin j representations of SL(2,R), which is interpreted as the isometry group of the hyperbolic upper half-plane. We also discuss the connection with the Hamiltonian reduction of SL(2,R)_k WZNW model to Liouville theory. • Yu Nakayama 2004年9月3日 詳細を見る We construct crosscap states in the N = 2 Liouville theory from the modular bootstrap method. We verify our results by comparing it with the calculation from the minisuperspace approximation and by checking the consistency with the conformal bootstrap equation. Various overlaps with other known branes are studied. We further discuss the topological nature of the discrete terms in the crosscap wavefunction and their connection with the Landau-Ginzburg approach in a nontrivial dilaton background. We find that it can be mapped to the Landau-Ginzburg theory with a negative power superpotential by a simple change of variables, extending the known duality to the open string sector. Possible applications to the two-dimensional noncritical string theories and supersymmetric orientifolds in the higher dimension are also discussed. • Yu Nakayama, Yuji Sugawara, Hiromitsu Takayanagi 2004年6月21日 詳細を見る In this paper we construct the time dependent boundary states describing the `rolling D-brane solutions'' in the NS5 background discovered recently by Kutasov by means of the classical DBI analysis. We first survey some aspects of non-compact branes in the NS5 background based on known boundary states in the N=2 Liouville theory. We consider two types of non-compact branes, one of which is BPS and the other is non-BPS but stable. Then we clarify how to Wick-rotate the non-BPS one appropriately. We show that the Wick-rotated boundary state realizes the correct trajectory of rolling D-brane in the classical limit, and leads to well behaved spectral densities of open strings due to the existence of non-trivial damping factors of energy. We further study the cylinder amplitudes and the emission rates of massive closed string modes. • Gaetano Bertoldi, Stefano Bolognesi, Marco Matone, Luca Mazzucato, Yu Nakayama 2004年5月12日 詳細を見る We study the instanton contributions of N=2 supersymmetric gauge theory and propose that the instanton moduli space is mapped to the moduli space of punctured spheres. Due to the recursive structure of the boundary in the Deligne-Knudsen-Mumford stable compactification, this leads to a new recursion relation for the instanton coefficients, which is bilinear. Instanton contributions are expressed as integrals on M_{0,n} in the framework of the Liouville F-models. This also suggests considering instanton contributions as a kind of Hurwitz numbers and also provides a prediction on the asymptotic form of the Gromov-Witten invariants. We also interpret this map in terms of the geometric engineering approach to the gauge theory, namely the topological A-model, as well as in the noncritical string theory framework. We speculate on the extension to nontrivial gravitational background and its relation to the uniformization program. Finally we point out an intriguing analogy with the self-dual YM equations for the gravitational version of SU(2) where surprisingly the same Hauptmodule of the SW solution appears. • Yu Nakayama 2004年2月2日 詳細を見る We review recent developments (up to January 2004) of the Liouville field theory and its matrix model dual. This review consists of three parts. In part I, we review the bosonic Liouville theory. After briefly reviewing the necessary background, we discuss the bulk structure constants (the DOZZ formula) and the boundary states (the FZZT brane and the ZZ brane). Various applications are also presented. In part II, we review the supersymmetric extension of the Liouville theory. We first discuss the bulk structure constants and the branes as in the bosonic Liouville theory, and then we present the matrix dual descriptions with some applications. In part III, the Liouville theory on unoriented surfaces is reviewed. After introducing the crosscap state, we discuss the matrix model dual description and the tadpole cancellation condition. This review also includes some original material such as the derivation of the conjectured dual action for the N = 2 Liouville theory from other known dualities and the comparison of the Liouville crosscap state with the c = 0 unoriented matrix model. This is based on my master's thesis submitted to Department of Physics, Faculty of Science, University of Tokyo on January 2004. • Yu Nakayama 2003年9月5日 詳細を見る The tadpole cancellation in the unoriented Liouville theory is discussed. Using two different methods -- the free field method and the boundary-crosscap state method, we derive one-loop divergences. Both methods require two D1-branes with the symplectic gauge group to cancel the orientifold tadpole divergence. However, the finite part left is different in each method and this difference is studied. We also discuss the validity of the free field method and the possible applications of our result. • Yu Nakayama 2003年6月2日 詳細を見る We propose an efficient way to obtain a correct Veneziano-Yankielowicz type integration constant of the effective glueball superpotential$W_{eff}(S,g,\Lambda)$, even for massless theories. Applying our method, we show some$\mathcal{N} = 1$theories do not have such an effective glueball superpotential, even though they have isolated vacua. In these cases,$S = 0$typically. ### MISC • Koichiro Nakagawa, Yu Nakayama 2021年3月18日 詳細を見る We show that CP-violating Weyl anomaly induces a supersymmetry anomaly in the formulation of superconformal supergravity as is observed in CP-preserving cases. This supersymmetry anomaly can be removed in the old minimal supergravity by adding suitable local counterterms, and it becomes a consistent theory. • Yu Nakayama 2021年1月8日 詳細を見る Recently a non-supersymmetric conformal field theory with an exactly marginal deformation in the large$N$limit was constructed by Chaudhuri-Choi-Rabinovici. On a non-supersymmetric conformal manifold,$c\$
coefficient of the trace anomaly in four dimensions would generically change.
In this model, we, however, find that it does not change at the first
non-trivial order given by three-loop diagrams.

### 書籍等出版物

• 高次元共形場理論への招待―3次元臨界Ising模型を解く

中山 優（ 担当： 単著）

サイエンス社  2019年11月1日

詳細を見る

記述言語：日本語 著書種別：学術書

### 共同研究・競争的資金等の研究

• 共形ブートストラップ

その他の研究制度

詳細を見る

2014年4月 - 現在

資金種別：競争的資金

• 高次元共形場理論、特に共形ブートストラップで探る量子重力理論の無矛盾性

日本学術振興会  科学研究費助成事業 基盤研究(C)

中山 優

詳細を見る

2021年4月 - 2026年3月

課題番号：21K03581

配分額：4160000円 （ 直接経費：3200000円 、 間接経費：960000円 ）

• 共形ブートストラップで解く量子色力学のカイラル相転移現象

日本学術振興会  科学研究費助成事業 若手研究(B)

中山 優

詳細を見る

2017年4月 - 2021年3月

課題番号：17K14301

配分額：4160000円 （ 直接経費：3200000円 、 間接経費：960000円 ）

本研究の眼目は共形対称性を元にしてQCDのカイラル相転移などの物理的に重要な相転移の性質を求めることである。本年度は、次の３点に注目して研究した。１．共形対称性を持った場の理論の性質を深く理解する。２．QCDのカイラル相転移が持つ対称性の性質を理論的に理解する。３．QCDの相転移に対して共形ブートストラップを適用することを考える。
１の点については、射影空間上での共形場理論の性質や、あるいはポワンカレ対称性がないような場の量子論においての共形対称性の定義やその性質など、新しい場の理論の知見を得ることに成功した。また、共形場理論に現れるアノマリーに新しい性質のものが存在するのではないか？という観点からの研究もはじめている。
２の点に関しては、格子シミュレーションの専門家と共同で、QCDのカイラル対称性が過去に考えられていたSU(2)の対称性の回復に伴って、アノマリーで破れていたU(1)対称性も回復するのではないか？という知見を得て、それが共形場理論に対してどのように影響を与えるのか調べた。また、QCDの拡張としてフレーバーの数を増やしていった時にどのような性質の共形場理論が現れるのか、あるいは、高次元で同じようなことが起こるのかと言う観点からも数値的な理解を進めた。
３は現在進行中であり、既存の方法だけではなく新しいアイディアを取り入れてQCDの相転移の性質、とりわけ、その次数や臨界指数などを明らかにしていきたいと考えている。

• ブラックホール・ストリング相転移に基づいた量子重力とタキオン凝縮の物理

日本学術振興会  科学研究費助成事業 特別研究員奨励費

中山 優

詳細を見る

2007年 - 2009年

課題番号：07J01841

配分額：1200000円 （ 直接経費：1200000円 ）

1、超対称共形場理論の素粒子現象への応用。
超対称性を持つ素粒子標準模型の拡張において、1eV程度の軽いグラヴィティーノを予言する模型の構築は現象論的に大きな意義を持つ。申請者は、超共形場理論を基礎においた、新しいクラスのゲージ的伝達機構を提案し、軽いグラヴィティーノを実現する模型を、実際に構築した。
2、4次元超共形代数の指数の研究。
4次元共形場理論の分類において、指数の計はもっと基礎的で重要である。申請者は、Lare N極限を超えて、有限のゲージ群のランクでも指数が具体的に計算できるような、新しい極限を提案し、ゲージ、重力対応を通して、その新しい趣限の重力的な起源を解明した。
3、Unarticle Phsicsの研究。
共形不変な場の理論が現実に存在している場合、その物理的な帰結はUnparticle Physicsとして、加速器実験における特異な予言をする。申請者は、超対称性が現実に存在すると仮定した上で、Unparticleセクターと共存する可能性を議論した。一般に、超対称性が破れていると、その影響でUnparticleセクターの共形不変性が壊れる。この共形不変性の破れが小さくなる要請は、超対称性の破れの伝達に大きな制限を与えるととを示した。
4、宇宙の始まりの特異性の解消の研究。
宇宙の始まりの特異性を除去する方法を探ることは、超弦理論に課せられた一つの使命である。申請者は、次元の異なる空間の間の新しいデュアリティ(D-duality)を通して、宇宙の始まりの特異性を除去する可能性を議論した。特に、D-dualityにおけるD-braneの振る舞いを考察した。

• 非臨界弦理論とそれを応用した超弦理論の研究

日本学術振興会  科学研究費助成事業 特別研究員奨励費

中山 優

詳細を見る

2005年 - 2006年

課題番号：05J11178

配分額：1900000円 （ 直接経費：1900000円 ）

1.2次元ブラックホール中を運動するD-braneの研究。2次元ブラックホール中を運動するD-braneを厳密に記述する境界状態を構成し、その物理的性質を調べた。特に、open-closed dualityとunitarityの両立性を厳密に示し、世界面上でのWick rotationの正しい取り扱い法を確立した。これによって、本研究者が昨年度に提唱した境界状態の構築法の正当性が明らかになった。また、量子重力的な相転移を厳密な弦理論の枠内で発見し、その具体的な性質を、境界状態を用いることで詳しく解析した。
2.4次元超共形場理論の現象論への応用。4次元共形揚の理論を基礎にした新しい超対称性の伝達の破れの機構"conformal gauge mediation"を提唱した。このモデルは余計なパラメタを含まず、さらに超対称粒子に対して独自のスペクトラムの予言をするために、完全に実験によって、検証可能である。特に、軽いグラヴィティーノを予言するなど現象論的にも面白いモデルになっている。