2022/05/25 更新

ハツダ　ヤスユキ

HATSUDA Yasuyuki
*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）

• 数理物理学の研究を主に行っている。特に場の量子論や超弦理論の背後に存在する数学的な構造に興味を持っている。現在は主に、超対称性を持つ場の量子論の厳密な解析とブラックホール物理への応用、摂動論における非摂動的性質の解析、弦理論の物性系への応用、厳密に解ける模型の解析などの研究テーマに取り組んでいる。

• 担当科目*
2022年度
学内職務経歴*
• 2021年4月 - 現在
理学部   物理学科   准教授
• 2021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
• 2021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
• 2017年4月 - 2021年3月
理学部   物理学科   助教

### 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

• 2021年4月 - 現在
立教大学   理学部 物理学科   准教授

詳細を見る

• 2017年4月 - 2021年3月
立教大学   理学部 物理学科   助教

詳細を見る

• 2015年10月 - 2017年3月
ジュネーブ大学 リサーチ・アシスタント

詳細を見る

• 2013年10月 - 2015年9月
ドイツ電子シンクロトロン リサーチ・フェロー

詳細を見る

• 2012年10月 - 2013年9月
ドイツ電子シンクロトロン 訪問研究員

詳細を見る

• 2012年4月 - 2013年9月
東京工業大学大学院大学院理工学研究科 日本学術振興会 特別研究員 (PD)

詳細を見る

• 2010年4月 - 2012年3月
京都大学基礎物理学研究所 研究員

詳細を見る

• 2009年4月 - 2010年3月
理化学研究所 川合理論物理学研究室 日本学術振興会 特別研究員 (PD)

詳細を見る

• 2008年4月 - 2009年3月
東京大学大学院理学系研究科 日本学術振興会 特別研究員 (DC2)

詳細を見る

### 学歴

• 2004年4月 - 2009年3月
東京大学大学院理学系研究科物理学専攻

詳細を見る

• 2000年4月 - 2004年3月
東京大学工学部物理工学科

詳細を見る

### 受賞

• 2015年
素粒子奨学会 中村誠太郎賞

詳細を見る

### 論文

SciPost Physics12 ( 1 )   2022年1月5日

詳細を見る

掲載種別：研究論文（学術雑誌）   出版者・発行元：Stichting SciPost

We analytically study the Fermi-gas formulation of sphere correlation
functions of the Coulomb branch operators for 3d
<inline-formula><alternatives><tex-math>\mathcal{N}=4</tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mstyle mathvariant="script"><mml:mi>𝒩</mml:mi></mml:mstyle><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>
ADHM theory with a gauge group <inline-formula><alternatives><tex-math>U(N)</tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>U</mml:mi><mml:mo stretchy="false" form="prefix">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false" form="postfix">)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>,
an adjoint hypermultiplet and <inline-formula><alternatives><tex-math>l</tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>l</mml:mi></mml:math></alternatives></inline-formula>
hypermultiplets which can describe a stack of
<inline-formula><alternatives><tex-math>N</tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math></alternatives></inline-formula>
M2-branes at <inline-formula><alternatives><tex-math>A_{l-1}</tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>l</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>
singularities. We find that the leading coefficients of the perturbative
grand canonical correlation functions are invariant under a hidden
triality symmetry conjectured from the twisted M-theory. The triality
symmetry also helps us to fix the next-to-leading corrections
analytically.

• Yasuyuki Hatsuda, Masashi Kimura

Universe7 ( 12 ) 476 - 476   2021年12月4日

詳細を見る

掲載種別：研究論文（学術雑誌）   出版者・発行元：MDPI AG

This is an unconventional review article on spectral problems in black hole perturbation theory. Our purpose is to explain how to apply various known techniques in quantum mechanics to such spectral problems. The article includes analytical/numerical treatments, semiclassical perturbation theory, the (uniform) WKB method and useful mathematical tools: Borel summations, Padé approximants, and so forth. The article is not comprehensive, but rather looks into a few examples from various points of view. The techniques in this article are widely applicable to many other examples.

• Yasuyuki Hatsuda

General Relativity and Gravitation53 ( 10 ) 93   2021年10月

詳細を見る

掲載種別：研究論文（学術雑誌）   出版者・発行元：Springer Science and Business Media LLC

• Quasinormal modes of Kerr-de Sitter black holes via the Heun function

Yasuyuki Hatsuda

CLASSICAL AND QUANTUM GRAVITY38 ( 2 )   2021年1月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：IOP PUBLISHING LTD

This note addresses quasinormal mode (QNM) frequencies of four-dimensional asymptotically de Sitter rotating black holes. The main motivation is that Mathematica 12.1 has implemented a new family of special functions: Heun functions. Using the fact that Teukolsky's equations for Kerr-de Sitter black holes are mapped to Heun's equations, we are able to compute their QNM frequencies by the Heun function. In this approach, Mathematica normally evaluates these frequencies to arbitrary numerical precision in a few seconds. We further discuss an application to asymptotically flat rotating black holes.

• Semi-analytic expressions for quasinormal modes of slowly rotating Kerr black holes

Yasuyuki Hatsuda, Masashi Kimura

PHYSICAL REVIEW D102 ( 4 )   2020年8月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：AMER PHYSICAL SOC

We provide semi-analytic expressions for quasinormal mode frequencies of slowly rotating Kerr black holes to the quadratic order in the rotation parameter. We apply the parametrized black hole quasinormal mode ringdown formalism to the Chandrasekhar-Detweiler equation and the Sasaki-Nakamura equation instead of the Teukolsky equation, and compare our result with the previous numerical calculations.

• Bloch electrons on honeycomb lattice and toric Calabi-Yau geometry

Yasuyuki Hatsuda, Yuji Sugimoto

JOURNAL OF HIGH ENERGY PHYSICS ( 5 )   2020年5月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

We find a new relation between the spectral problem for Bloch electrons on a two-dimensional honeycomb lattice in a uniform magnetic field and that for quantum geometry of a toric Calabi-Yau threefold. We show that a difference equation for the Bloch electron is identical to a quantum mirror curve of the Calabi-Yau threefold. As an application, we show that bandwidths of the electron spectra in the weak magnetic flux regime are systematically calculated by the topological string free energies at conifold singular points in the Nekrasov-Shatashvili limit.

• Quasinormal modes of black holes and Borel summation

Yasuyuki Hatsuda

PHYSICAL REVIEW D101 ( 2 )   2020年1月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：AMER PHYSICAL SOC

We propose a simple and efficient way to compute quasinormal frequencies of spherically symmetric black holes. We revisit an old idea that relates them to bound state energies of anharmonic oscillators by an analytic continuation. This connection enables us to achieve remarkable high-order computations of WKB series by Rayleigh-Schrodinger perturbation theory. The known WKB results are easily reproduced. Our analysis shows that the perturbative WKB series of the quasinormal frequencies turns out to be a Borel summable divergent series both for the Schwarzschild and for the Reissner-Nordstrom black holes. Their Borel sums reproduce the correct numerical values.

• Instantons in the Hofstadter butterfly: difference equation, resurgence and quantum mirror curves

Zhihao Duan, Jie Gu, Yasuyuki Hatsuda, Tin Sulejmanpasic

JOURNAL OF HIGH ENERGY PHYSICS ( 1 )   2019年1月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

We study the Harper-Hofstadter Hamiltonian and its corresponding non-perturbative butterfly spectrum. The problem is algebraically solvable whenever the magnetic flux is a rational multiple of 2. For such values of the magnetic flux, the theory allows a formulation with two Bloch or -angles. We treat the problem by the path integral formulation, and show that the spectrum receives instanton corrections. Instantons as well as their one loop fluctuation determinants are found explicitly and the finding is matched with the numerical band width of the butterfly spectrum. We extend the analysis to all 2-instanton sectors with different -angle dependence to leading order and show consistency with numerics. We further argue that the instanton-anti-instanton contributions are ambiguous and cancel the ambiguity of the perturbation series, as they should. We hint at the possibility of exact 2-instanton solutions responsible for such contributions via Picard-Lefschetz theory. We also present a powerful way to compute the perturbative fluctuations around the 1-instanton saddle as well as the instanton-anti-instanton ambiguity by using the topological string formulation.

• Exact quantization conditions for the elliptic Ruijsenaars-Schneider model

Yasuyuki Hatsuda, Antonio Sciarappa, Szabolcs Zakany

JOURNAL OF HIGH ENERGY PHYSICS ( 11 )   2018年11月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

We propose and test exact quantization conditions for the N-particle quantum elliptic Ruijsenaars-Schneider integrable system, as well as its Calogero-Moser limit, based on the conjectural correspondence to the five-dimensional N = 1* SU(N) gauge theory in the Nekrasov-Shatashvili limit. We discuss two natural sets of quantization conditions, related by the electro-magnetic duality, and the importance of non-perturbative corrections in the Planck constant. We also comment on the eigenfunction problem, by reinterpreting the Separation of Variables approach in gauge theory terms.

• Perturbative/nonperturbative aspects of Bloch electrons in a honeycomb lattice

Yasuyuki Hatsuda

PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS2018 ( 9 )   2018年9月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：OXFORD UNIV PRESS INC

We revisit the spectral problem for Bloch electrons in a two-dimensional bipartite honeycomb lattice under a uniform magnetic field. It is well known that such a honeycomb structure is realized in graphene. We present a systematic framework to compute the perturbative magnetic flux expansions near two distinct band edges. We then analyze the nonperturbative bandwidth of the spectrum. It turns out that there is a novel similarity between the spectrum near the Dirac point in the honeycomb lattice and the spectrum in the supersymmetric sine-Gordon quantum mechanics. We finally confirm a nontrivial vacuum-instanton-bion threesome relationship. Our analysis heavily relies on numerical experiments.

• S-duality resurgence in SL(2) Chern-Simons theory

Dongmin Gang, Yasuyuki Hatsuda

JOURNAL OF HIGH ENERGY PHYSICS ( 7 )   2018年7月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

We find that an S-duality in SL(2) Chern-Simons theory for hyperbolic 3-manifolds emerges by the Borel resummation of a semiclassical expansion around a particular flat connection associated to the hyperbolic structure. We demonstrate it numerically with two representative examples of hyperbolic 3-manifolds.

• Calabi-Yau geometry and electrons on 2d lattices

Yasuyuki Hatsuda, Yuji Sugimoto, Zhaojie Xu

PHYSICAL REVIEW D95 ( 8 )   2017年4月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：AMER PHYSICAL SOC

The B-model approach of topological string theory leads to difference equations by quantizing algebraic mirror curves. It is known that these quantum mechanical systems are solved by the refined topological strings. Recently, it was pointed out that the quantum eigenvalue problem for a particular Calabi-Yau manifold, known as local F-0, is closely related to the Hofstadter problem for electrons on a two-dimensional square lattice. In this paper, we generalize this idea to a more complicated Calabi-Yau manifold. We find that the local B-3 geometry, which is a three-point blow-up of local P-2, is associated with electrons on a triangular lattice. This correspondence allows us to use known results in condensed matter physics to investigate the quantum geometry of the toric Calabi-Yau manifold.

• Topological Strings from Quantum Mechanics

Alba Grassi, Yasuyuki Hatsuda, Marcos Mario

ANNALES HENRI POINCARE17 ( 11 ) 3177 - 3235   2016年11月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER INTERNATIONAL PUBLISHING AG

We propose a general correspondence which associates a non-perturbative quantum-mechanical operator to a toric Calabi-Yau manifold, and we conjecture an explicit formula for its spectral determinant in terms of an M-theoretic version of the topological string free energy. As a consequence, we derive an exact quantization condition for the operator spectrum, in terms of the vanishing of a generalized theta function. The perturbative part of this quantization condition is given by the Nekrasov-Shatashvili limit of the refined topological string, but there are non-perturbative corrections determined by the conventional topological string. We analyze in detail the cases of local , local and local . In all these cases, the predictions for the spectrum agree with the existing numerical results. We also show explicitly that our conjectured spectral determinant leads to the correct spectral traces of the corresponding operators. Physically, our results provide a non-perturbative formulation of topological strings on toric Calabi-Yau manifolds, in which the genus expansion emerges as a 't Hooft limit of the spectral traces. Since the spectral determinant is an entire function on moduli space, it leads to a background-independent formulation of the theory. Mathematically, our results lead to precise, surprising conjectures relating the spectral theory of functional difference operators to enumerative geometry.

• Hofstadter's butterfly in quantum geometry

Yasuyuki Hatsuda, Hosho Katsura, Yuji Tachikawa

NEW JOURNAL OF PHYSICS18   2016年10月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：IOP PUBLISHING LTD

We point out that the recent conjectural solution to the spectral problem for the Hamiltonian H = e(x) + e (x) + e(p) + e (p) in terms of the refined topological invariants of a local Calabi-Yau (CY) geometry has an intimate relation with two-dimensional non-interacting electrons moving in a periodic potential under a uniform magnetic field. In particular, we find that the quantum A-period, determining the relation between the energy eigenvalue and the Kehler modulus of the CY, can be found explicitly when the quantum parameter q = e(i (h) over bar) is a root of unity, that its branch cuts are given by Hofstadter's butterfly, and that its imaginary part counts the number of states of the Hofstadter Hamiltonian. The modular double operation, exchanging (h) over bar and = <(<(h)over tilde>)over bar> = 4 pi(2)/(h) over bar, plays an important role.

• Exact results for ABJ Wilson loops and open-closed duality

Yasuyuki Hatsuda, Kazumi Okuyama

JOURNAL OF HIGH ENERGY PHYSICS ( 10 )   2016年10月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

We find new exact relations between the partition function and vacuum expectation values (VEVs) of 1/2 BPS Wilson loops in ABJ theory, which allow us to predict the large N expansions of the 1/2 BPS Wilson loops from known results of the partition function. These relations are interpreted as an open-closed duality where the closed string background is shifted by the insertion of Wilson loops due to a back-reaction. Using the connection between ABJ theory and the topological string on local P-1 x P-1, we explicitly write down non-trivial relations between open and closed string amplitudes.

• ABJM on ellipsoid and topological strings

Yasuyuki Hatsuda

JOURNAL OF HIGH ENERGY PHYSICS ( 7 )   2016年7月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

It is known that the large N expansion of the partition function in ABJM theory on a three- sphere is completely determined by the topological string on local Hirzebruch surface F-0. In this note, we investigate the ABJM partition function on an ellipsoid, which has a conventional deformation parameter b. Using 3d mirror symmetry, we find a remarkable relation between the ellipsoid partition function for b(2) = 3 (or b(2) = 1/3) in ABJM theory at k = 1 and a matrix model for the topological string on another Calabi-Yau threefold, known as local P-2. As in the case of b = 1, we can compute the full large N expansion of the partition function in this case. This is the first example of the complete large N solution in ABJM theory on the squashed sphere. Using the obtained results, we also analyze the supersymmetric Renyi entropy.

• Exact quantization conditions for cluster integrable systems

Sebastian Franco, Yasuyuki Hatsuda, Marcos Marino

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT   2016年6月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：IOP PUBLISHING LTD

We propose exact quantization conditions for the quantum integrable systems of Goncharov and Kenyon, based on the enumerative geometry of the corresponding toric Calabi-Yau manifolds. Our conjecture builds upon recent results on the quantization of mirror curves, and generalizes a previous proposal for the quantization of the relativistic Toda lattice. We present explicit tests of our conjecture for the integrable systems associated to the resolved C-3/Z(5) and C-3/Z(6) orbifolds.

• Exact quantization conditions for the relativistic Toda lattice

Yasuyuki Hatsuda, Marcos Marino

JOURNAL OF HIGH ENERGY PHYSICS ( 5 )   2016年5月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

Inspired by recent connections between spectral theory and topological string theory, we propose exact quantization conditions for the relativistic Toda lattice of N particles. These conditions involve the Nekrasov-Shatashvili free energy, which resums the perturbative WKB expansion, but they require in addition a non-perturbative contribution, which is related to the perturbative result by an S-duality transformation of the Planck constant. We test the quantization conditions against explicit calculations of the spectrum for N = 3. Our proposal can be generalized to arbitrary toric Calabi-Yau manifolds and might solve the corresponding quantum integrable system of Goncharov and Kenyon.

• Quantization conditions and functional equations in ABJ(M) theories

Alba Grassi, Yasuyuki Hatsuda, Marcos Marino

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL49 ( 11 )   2016年3月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：IOP PUBLISHING LTD

The partition function of ABJ(M) theories on the three-sphere can be regarded as the canonical partition function of an ideal Fermi gas with a non-trivial Hamiltonian. We propose an exact expression for the spectral determinant of this Hamiltonian, which generalizes recent results obtained in the maximally supersymmetric case. As a consequence, we find an exact WKB quantization condition determining the spectrum which is in agreement with numerical results. In addition, we investigate the factorization properties and functional equations for our conjectured spectral determinants. These functional equations relate the spectral determinants of ABJ theories to consecutive ranks of gauge groups but the same Chern-Simons coupling.

• Spectral zeta function and non-perturbative effects in ABJM Fermi-gas

Yasuyuki Hatsuda

JOURNAL OF HIGH ENERGY PHYSICS ( 11 )   2015年11月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

The exact partition function in ABJM theory on three-sphere can be regarded as a canonical partition function of a non-interacting Fermi-gas with an unconventional Hamiltonian. All the information on the partition function is encoded in the discrete spectrum of this Hamiltonian. We explain how (quantum mechanical) non-perturbative corrections in the Fermi-gas system appear from a spectral consideration. Basic tools in our analysis are a Mellin-Barnes type integral representation and a spectral zeta function. From a consistency with known results, we conjecture that the spectral zeta function in the ABJM Fermi-gas has an in finite number of "non-perturbative" poles, which are invisible in the semi-classical expansion of the Planck constant. We observe that these poles indeed appear after summing up perturbative corrections. As a consequence, the perturbative resummation of the spectral zeta function causes non-perturbative corrections to the grand canonical partition function. We also present another example associated with a spectral problem in topological string theory. A conjectured non-perturbative free energy on the resolved conifold is successfully reproduced in this framework.

• Exact instanton expansion of the ABJM partition function

Yasuyuki Hatsuda, Sanefumi Moriyama, Kazumi Okuyama

PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS2015 ( 11 )   2015年11月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：OXFORD UNIV PRESS INC

We review recent progress in determining the partition function of the ABJM theory in the large-N expansion, including all of the perturbative and non-perturbative corrections. In particular, we focus on how these exact expansions are obtained from various beautiful relations to the Fermi gas system, topological string theory, the integrable model, and the supergroup.

• Resurgence of the cusp anomalous dimension

Daniele Dorigoni, Yasuyuki Hatsuda

JOURNAL OF HIGH ENERGY PHYSICS ( 9 )   2015年9月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

We revisit the strong coupling limit of the cusp anomalous dimension in planar N = 4 super Yang-Mills theory. It is known that the strong coupling expansion is asymptotic and non-Borel summable. As a consequence, the cusp anomalous dimension receives non-perturbative corrections, and the complete strong coupling expansion should be a resurgent transseries. We reveal that the perturbative and non-perturbative parts in the transseries are closely interrelated. Solving the Beisert-Eden-Staudacher equation systematically, we analyze in detail the large order behavior in the strong coupling perturbative expansion and show that the non-perturbative information is indeed encoded there. An ambiguity of (lateral) Borel resummations of the perturbative expansion is precisely canceled by the contributions from the non-perturbative sectors, and the final result is real and unambiguous.

• Large N non-perturbative effects in N=4 superconformal Chern-Simons theories

Yasuyuki Hatsuda, Masazumi Honda, Kazumi Okuyama

JOURNAL OF HIGH ENERGY PHYSICS ( 9 )   2015年9月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

We investigate the large N instanton effects of partition functions in a class of N = 4 circular quiver Chern-Simons theories on a three-sphere. Our analysis is based on the supersymmetry localization and the Fermi-gas formalism. The resulting matrix model can be regarded as a two-parameter deformation of the ABJM matrix model, and has richer non-perturbative structures. Based on a systematic semi-classical analysis, we find analytic expressions of membrane instanton corrections. We also exactly compute the partition function for various cases and find some exact forms of worldsheet instanton corrections, which appear as quantum mechanical non-perturbative corrections in the Fermi-gas system.

• Resummations and non-perturbative corrections

Yasuyuki Hatsuda, Kazumi Okuyama

JOURNAL OF HIGH ENERGY PHYSICS ( 9 )   2015年9月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

We consider a generalization of the Borel resummation, which turns out to be equivalent to the standard Borel resummation. We apply it to the simplest large N duality between the pure Chern-Simons theory and the topological string on the resolved conifold, and obtain a simple integral formula for the free energy. Expanding this integral representation around the large radius point at finite string coupling g(s), we find that it includes not only the M-theoretic resummation a la Gopakumar and Vafa, but also a non-perturbative correction in g(s). Remarkably, the obtained non-perturbative correction is in perfect agreement with a proposal for membrane instanton corrections in arXiv: 1306.1734. Various other examples are also presented.

• Wilson loop OPE, analytic continuation and multi-Regge limit

Yasuyuki Hatsuda

JOURNAL OF HIGH ENERGY PHYSICS ( 10 )   2014年10月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

We explore a direct connection between the collinear limit and the multi-Regge limit for scattering amplitudes in the N = 4 super Yang-Mills theory. Starting with the collinear expansion for the six-gluon amplitude in the Euclidean kinematic region, we perform an analytic continuation term by term to the so-called Mandelstam region. We find that the result coincides with the collinear expansion of the analytically continued amplitude. We then take the multi-Regge limit, and conjecture that the final result precisely reproduces the one from the BFKL approach. Combining this procedure with the OPE for null polygonal Wilson loops, we explicitly compute the leading contribution in the "collinear-Regge" limit up to five loops. Our results agree with all the known results up to four loops. At five-loop, our results up to the next-to-next-to-leading logarithmic approximation (NNLLA) also reproduce the known results, and for the N(3)LLA and the N(4)LLA give non-trivial predictions. We further present an all-loop prediction for the imaginary part of the next-to-double-leading logarithmic approximation. Our procedure has a possibility of an interpolation from weak to strong coupling in the multi-Regge limit with the help of the OPE.

• Probing non-perturbative effects in M-theory

Yasuyuki Hatsuda, Kazumi Okuyama

JOURNAL OF HIGH ENERGY PHYSICS ( 10 )   2014年10月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

The AdS/CFT correspondence enables us to probe M-theory on various backgrounds from the corresponding dual gauge theories. Here we investigate in detail a three-dimensional U(N) N = 4 super Yang-Mills theory coupled to one adjoint hypermultiplet and N-f fundamental hypermultiplets, which is large N dual to M-theory on AdS(4)xS(7)/Z(Nf). Using the localization and the Fermi-gas formulation, we explore non-perturbative corrections to the partition function. As in the ABJM theory, we find that there exists a non-trivial pole cancellation mechanism, which guarantees the theory to be well-defined, between worldsheet instantons and membrane instantons for all rational (in particular, physical or integral) values of N-f.

• Non-perturbative effects and the refined topological string

Yasuyuki Hatsuda, Marcos Marino, Sanefumi Moriyama, Kazumi Okuyama

JOURNAL OF HIGH ENERGY PHYSICS ( 9 )   2014年9月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

The partition function of ABJM theory on the three-sphere has nonperturbative corrections due to membrane instantons in the M-theory dual. We show that the full series of membrane instanton corrections is completely determined by the refined topological string on the Calabi-Yau manifold known as local P-1 x P-1, in the Nekrasov-Shatashvili limit. Our result can be interpreted as a first-principles derivation of the full series of non-perturbative effects for the closed topological string on this Calabi-Yau background. Based on this, we make a proposal for the non-perturbative free energy of topological strings on general, local Calabi-Yau manifolds.

• Quantum Wronskian approach to six-point gluon scattering amplitudes at strong coupling

Yasuyuki Hatsuda, Katsushi Ito, Yuji Satoh, Junji Suzuki

JOURNAL OF HIGH ENERGY PHYSICS ( 8 )   2014年8月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

We study the six-point gluon scattering amplitudes in N = 4 super YangMills theory at strong coupling based on the twisted Z(4)-symmetric integrable model. The lattice regularization allows us to derive the associated thermodynamic Bethe ansatz (TBA) equations as well as the functional relations among the Q-/T-/Y-functions. The quantum Wronskian relation for the Q-/T-functions plays an important role in determining a series of the expansion coefficients of the T-/Y-functions around the UV limit, including the dependence on the twist parameter. Studying the CFT limit of the TBA equations, we derive the leading analytic expansion of the remainder function for the general kinematics around the limit where the dual Wilson loops become regular-polygonal. We also compare the rescaled remainder functions at strong coupling with those at two, three and four loops, and find that they are close to each other along the trajectories parameterized by the scale parameter of the integrable model.

• ABJM Wilson loops in arbitrary representations

Yasuyuki Hatsuda, Masazumi Honda, Sanefumi Moriyama, Kazumi Okuyama

JOURNAL OF HIGH ENERGY PHYSICS ( 10 )   2013年10月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

We study vacuum expectation values (VEVs) of circular half BPS Wilson loops in arbitrary representations in ABJM theory. We find that those in hook representations are reduced to elementary integrations thanks to the Fermi gas formalism, which are accessible from the numerical studies similar to the partition function in the previous studies. For non-hook representations, we show that the VEVs in the grand canonical formalism can be exactly expressed as determinants of those in the hook representations. Using these facts, we can study the instanton effects of the VEVs in various representations. Our results are consistent with the worldsheet instanton effects studied from the topological string and a prescription to include the membrane instanton effects by shifting the chemical potential, which has been successful for the partition function.

• Instanton bound states in ABJM theory

Yasuyuki Hatsuda, Sanefumi Moriyama, Kazumi Okuyama

JOURNAL OF HIGH ENERGY PHYSICS ( 5 )   2013年5月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

The partition function of the ABJM theory receives non-perturbative corrections due to instanton effects. We study these non-perturbative corrections, including bound states of worldsheet instantons and membrane instantons, in the Fermi-gas approach. We require that the total non-perturbative correction should be always finite for arbitrary Chern-Simons level. This finiteness is realized quite non-trivially because each bound state contribution naively diverges at some levels. The poles of each contribution should be canceled out in total. We use this pole cancellation mechanism to find unknown bound state corrections from known ones. We conjecture a general expression of the bound state contribution. Summing up all the bound state contributions, we find that the effect of bound states is simply incorporated into the worldsheet instanton correction by a redefinition of the chemical potential in the Fermi-gas system. Analytic expressions of the 3- and 4-membrane instanton corrections are also proposed.

• Null-polygonal minimal surfaces in AdS(4) from perturbed W minimal models

Yasuyuki Hatsuda, Katsushi Ito, Yuji Satoh

JOURNAL OF HIGH ENERGY PHYSICS ( 2 )   2013年2月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

We study the null-polygonal minimal surfaces in AdS(4), which correspond to the gluon scattering amplitudes/Wilson loops in N = 4 super Yang-Mills theory at strong coupling. The area of the minimal surfaces with it cusps is characterized by the thermodynamic Bottle ansatz (TBA) integral equations or the Y-system of the homogeneous sine-Gordon model, which is regarded as the SU(n - 4)(4)/U(1)(n-5) generalized parafermion theory perturbed by the weight-zero adjoint operators. Based on the relation to the TBA systems of the perturbed W minimal models, we solve the TBA equations by using the conformal perturbation theory, and obtain the analytic expansion of the remainder function around the UV/regular-polygonal limit for n = 6 and 7. We compare the rescaled remainder function for n = 6 with the two-loop one, to observe that they are close to each other similarly to the AdS(3) case.

• Instanton effects in ABJM theory from Fermi gas approach

Yasuyuki Hatsuda, Sanefumi Moriyama, Kazumi Okuyama

JOURNAL OF HIGH ENERGY PHYSICS ( 1 )   2013年1月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

We study the instanton effects of the ABJM partition function using the Fermi gas formalism. We compute the exact values of the partition function at the Chern-Simons levels k = 1, 2, 3, 1, 6 up to N = 44,20,18, 16, 14 respectively, and extract non-perturbative corrections from these exact results. Fitting the resulting non-perturbative corrections by their expected forms from the Fermi gas, we determine unknown parameters in them. After separating the oscillating behavior of the grand potential, which originates in the periodicity of the grand partition function, and the worldsheet instanton contribution, which is computed from the topological string theory, we succeed in proposing an analytical expression for the leading D2-instanton correction. Just as the perturbative result, the instanton corrections to the partition function are expressed in terms of the Airy function.

• Exact results on the ABJM Fermi gas

Yasuyuki Hatsuda, Sanefumi Moriyama, Kazumi Okuyama

JOURNAL OF HIGH ENERGY PHYSICS ( 10 )   2012年10月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

We study the Fermi gas quantum mechanics associated to the ABJM matrix model. We develop a method to compute the grand partition function of the ABJM theory, and compute exactly the partition function Z (N) up to N = 9 with the Chern-Simons level k = 1. We find that the eigenvalue problem of this quantum mechanical system is reduced to the diagonalization of a certain Hankel matrix. In reducing the number of integrations by commuting coordinates and momenta, we find an exact relation concerning the grand partition function, which is interesting on its own right and very helpful for determining the partition function. We also study the TBA-type integral equations that allow us to compute the grand partition function numerically. Surprisingly, all of our exact partition functions are written in terms of polynomials of pi(-1) with rational coefficients.

• T-functions and multi-gluon scattering amplitudes

Yasuyuki Hatsuda, Katsushi Ito, Yuji Satoh

JOURNAL OF HIGH ENERGY PHYSICS ( 2 )   2012年2月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

We study gluon scattering amplitudes/Wilson loops in N = 4 super Yang-Mills theory at strong coupling which correspond to minimal surfaces with a light-like polygonal boundary in AdS(3). We find a concise expression of the remainder function in terms of the T-function of the associated thermodynamic Bethe ansatz (TBA) system. Continuing our previous work on the analytic expansion around the CFT/regular-polygonal limit, we derive a formula of the leading-order expansion for the general 2n-point remainder function. The T-system allows us to encode its momentum dependence in only one function of the TBA mass parameters, which is obtained by conformal perturbation theory. We compute its explicit form in the single mass cases. We also find that the rescaled remainder functions at strong coupling and at two loops are close to each other, and their ratio at the leading order approaches a constant near 0.9 for large n

• Probing AdS wormholes by entanglement entropy

Mitsutoshi Fujita, Yasuyuki Hatsuda, Tadashi Takayanagi

JOURNAL OF HIGH ENERGY PHYSICS ( 6 )   2011年6月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

In this paper, we study the Lorentzian AdS wormhole solutions constructed in arXiv:0808.2481 [hep-th]. Each of them is a classical solution interpolating between an AdS space and a flat space in type IIB supergravity. We calculate the holographic entanglement entropy to probe this geometry. Our analysis shows that there exits a mass gap in its holographic dual gauge theory and that the entanglement between the two boundaries is rather suppressed than that we naively expect for wormholes.

• g-functions and gluon scattering amplitudes at strong coupling

Yasuyuki Hatsuda, Katsushi Ito, Kazuhiro Sakai, Yuji Satoh

JOURNAL OF HIGH ENERGY PHYSICS ( 4 )   2011年4月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

We study gluon scattering amplitudes/Wilson loops in N = 4 super Yang-Mills theory at strong coupling by calculating the area of the minimal surfaces in AdS(3) based on the associated thermodynamic Bethe ansatz system. The remainder function of the amplitudes is computed by evaluating the free energy, the T- and Y-functions of the homogeneous sine-Gordon model. Using conformal field theory (CFT) perturbation, we examine the mass corrections to the free energy around the CFT point corresponding to the regular polygonal Wilson loop. Based on the relation between the T-functions and the g-functions, which measure the boundary entropy, we calculate corrections to the T-and Y-functions as well as express them at the CFT point by the modular S-matrix. We evaluate the remainder function around the CFT point for 8 and 10-point amplitudes explicitly and compare these analytic expressions with the 2-loop formulas. The two rescaled remainder functions show very similar power series structures.

• Six-point gluon scattering amplitudes from Z(4)-symmetric integrable model

Yasuyuki Hatsuda, Katsushi Ito, Kazuhiro Sakai, Yuji Satoh

JOURNAL OF HIGH ENERGY PHYSICS ( 9 )   2010年9月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

We study six-point gluon scattering amplitudes in N = 4 super Yang-Mills theory at strong coupling by investigating the thermodynamic Bethe ansatz equations of the underlying Z(4)-symmetric integrable model both analytically and numerically. By the conformal field theory (CFT) perturbation, we compute the free energy part of the remainder function with generic chemical potential near the CFT/small mass limit. Combining this with the expansion of the Y-functions, we obtain the remainder function near the small mass limit up to a function of the chemical potential, which can be evaluated numerically. We also find the leading corrections to the remainder function near the large mass limit. We confirm that these results are in good agreement with numerical computations.

• Thermodynamic Bethe ansatz equations for minimal surfaces in AdS(3)

Yasuyuki Hatsuda, Katsushi Ito, Kazuhiro Sakai, Yuji Satoh

JOURNAL OF HIGH ENERGY PHYSICS ( 4 )   2010年4月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

We study classical open string solutions with a null polygonal boundary in AdS(3) in relation to gluon scattering amplitudes in N = 4 super Yang-Mills at strong coupling. We derive in full detail the set of integral equations governing the decagonal and the dodecagonal solutions and identify them with the thermodynamic Bethe ansatz equations of the homogeneous sine-Gordon models. By evaluating the free energy in the conformal limit we compute the central charges, from which we observe general correspondence between the polygonal solutions in AdS(n) and generalized parafermions.

• Genus-one correction to asymptotically free Seiberg-Witten prepotential from Dijkgraaf-Vafa matrix model

Mitsutoshi Fujita, Yasuyuki Hatsuda, Ta-Sheng Tai

JOURNAL OF HIGH ENERGY PHYSICS ( 3 )   2010年3月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

We find perfect agreements on the genus-one correction to the prepotential of SU(2) Seiberg-Witten theory with N-f = 2, 3 between field theoretical and Dijkgraaf-Vafa-Penner type matrix model results.

• Scattering of giant magnons in CP3

Yasuyuki Hatsuda, Hiroaki Tanaka

JOURNAL OF HIGH ENERGY PHYSICS ( 2 )   2010年2月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

We study classical scattering phase of CP2 dyonic giant magnons in R-t x CP3. We construct two-soliton solutions explicitly by the dressing method. Using these solutions, we compute the classical time delays for the scattering of giant magnons, and compare them to boundstate S-matrix elements derived from the conjectured AdS(4)/CFT3 S-matrix by Ahn and Nepomechie in the strong coupling limit. Our result is consistent with the conjectured S-matrix. The dyonic solutions play an essential role in revealing the polarization dependence of scattering phase.

• Finite-size effects for dyonic giant magnons

Yasuyuki Hatsuda, Ryo Suzuki

NUCLEAR PHYSICS B800 ( 1-2 ) 349 - 383   2008年9月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：ELSEVIER

We compute finite-size corrections to dyonic giant magnons in two ways. One is by examining the asymptotic behavior of helical strings of [K. Okamura, R. Suzuki, A perspective on classical strings from complex sine-Gordon solitons, Phys. Rev. D 75 (2007) 046001, hep-th/0609026] as elliptic modulus k goes to unity, and the other is by applying the generalized Luscher formula for mu-term of [R.A. Janik, T Lukowski, Wrapping interactions at strong coupling-the giant magnon, Phys. Rev. D 76 (2007) 126008, arXiv: 0708.2208 [hep-th]] to the situation in which incoming particles are boundstates. By careful choice of poles in the sit(2 vertical bar 2)(2)-invariant S-matrix, we find agreement of the two results, which makes possible to predict the (leading) finite-size correction for dyonic giant magnons to all orders in the 't Hooft coupling. (c) 2008 Elsevier B.V. All rights reserved.

• Finite-size effects for multi-magnon states

Yasuyuki Hatsuda, Ryo Suzuki

JOURNAL OF HIGH ENERGY PHYSICS ( 9 )   2008年9月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

We propose the generalized Luscher formula for multi-magnon states by which one can compute the finite-size correction to the energy of multi giant magnons at classical and one-loop levels. It is shown that the F-term of our formula is consistent with the exact finite-size spectrum of the sinh-Gordon model, and the mu-term agrees with the finite-size energy of magnon boundstate of the asymptotic Bethe Ansatz in the su(2) sector at strong coupling. In an appendix, we evaluate our formula at weak coupling under some approximations, and find that the transcendental terms arise from a sum over an infinite tower of BPS boundstates.

• Finite-size corrections to dyonic giant magnons

Yasuyuki Hatsuda

INTERNATIONAL JOURNAL OF MODERN PHYSICS A23 ( 14-15 ) 2239 - 2240   2008年6月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：WORLD SCIENTIFIC PUBL CO PTE LTD

We compute finite-size corrections to dyonic giant magnons in two ways(1). One is by using classical string solutions corresponding to finite-size dyonic giant magnons called "helical strings". The other is by applying the Luscher formula known in relativistic quantum field theory to the case in which incoming particles are boundstates. We find these two methods lead the same result.

• Entanglement entropy in the Calogero-Sutherland model

Hosho Katsura, Yasuyuki Hatsuda

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL40 ( 46 ) 13931 - 13942   2007年11月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：IOP PUBLISHING LTD

We investigate the entanglement entropy between two subsets of particles in the ground state of the Calogero-Sutherland model. By using the duality relations of the Jack symmetric polynomials, we obtain exact expressions for both the reduced density matrix and the entanglement entropy in the limit of an infinite number of particles traced out. From these results, we obtain an upper-bound value of the entanglement entropy. This upper bound has a clear interpretation in terms of fractional exclusion statistics.

• Emergent classical strings from matrix model

Yasuyuki Hatsuda, Keisuke Okamura

JOURNAL OF HIGH ENERGY PHYSICS ( 3 )   2007年3月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER

Generalizing the idea of hep-th/0509015 by Berenstein, Correa, and Vazquez, we study many-magnon states in an SU( 2) sector of a reduced matrix quantum mechanics obtained from N = 4 SU( N) super Yang-Mills on R x S-3. Generic Q-magnon states are described as a chain of "string-bits" joining Q+1 eigenvalues of background matrices which form a 1/2 BPS circular droplet in the large N limit. We will concentrate on infinitely long states whose first and last eigenvalues localize at the edge of the droplet. Each constituent string-bit has a complex quasi-momentum in general, while the total quasi-momentum P of the state is real. For given Q and P, the minimum energy of the chain of string-bits is realized when the Q+1 eigenvalues are equally spaced on one and the same line segment joining the two outmost eigenvalues localized on the edge with angular difference P. Such configuration of bound string-bits precisely reproduces the dispersion relation for dyonic giant magnons in classical string theory. We also show the emergence of two-spin folded/circular strings in special infinite spin limit as particular configurations of closed chains of string-bits.

• Symmetry and integrability of non-singlet sectors in matrix quantum mechanics

Yasuyuki Hatsuda, Yutaka Matsuo

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL40 ( 7 ) 1633 - 1659   2007年2月

詳細を見る

記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：IOP PUBLISHING LTD

We study the non-singlet sectors of matrix quantum mechanics (MQM) through an operator algebra which generates the spectrum. The algebra is a nonlinear extension of the W-infinity algebra where the nonlinearity comes from the angular part of the matrix which cannot be neglected in the non-singlet sector. The algebra contains an infinite set of commuting generators which can be regarded as the conserved currents of MQM. We derive the spectrum and the eigenfunctions of these conserved quantities by a group theoretical method. An interesting feature of the spectrum of these charges in the non-singlet sectors is that they are identical to those of the singlet sector except for the multiplicities. We also derive the explicit form of these commuting charges in terms of the eigenvalues of the matrix and show that the interaction terms which are typical in Calogero Sutherland systems appear. Finally, we discuss the bosonization and rewrite the commuting charges in terms of a free boson together with a finite number of extra degrees of freedom for the non-singlet sectors.

### MISC

2021年7月5日

詳細を見る

We analytically study the Fermi-gas formulation of sphere correlation
functions of the Coulomb branch operators for 3d $\mathcal{N}=4$ ADHM theory
with a gauge group $U(N)$, an adjoint hypermultiplet and $l$ hypermultiplets
which can describe a stack of $N$ M2-branes at $A_{l-1}$ singularities. We find
that the leading coefficients of the perturbative grand canonical correlation
functions are invariant under a hidden triality symmetry conjectured from the
twisted M-theory. The triality symmetry also helps us to fix the

• Gleb Aminov, Alba Grassi, Yasuyuki Hatsuda

2020年6月10日

詳細を見る

We present new analytic results on black hole perturbation theory. Our
results are based on a novel relation to four-dimensional $\mathcal{N}=2$
supersymmetric gauge theories. We propose an exact version of Bohr-Sommerfeld
quantization conditions on quasinormal mode frequencies in terms of the
Nekrasov partition function in a particular phase of the $\Omega$-background.
Our quantization conditions also enable us to find exact expressions of
eigenvalues of spin-weighted spheroidal harmonics. We test the validity of our
conjecture by comparing against known numerical results for Kerr black holes as
well as for Schwarzschild black holes. Some extensions are also discussed.

### 共同研究・競争的資金等の研究

• 弦理論の幾何学とスペクトル理論

日本学術振興会  科学研究費助成事業 基盤研究(C)

初田 泰之

詳細を見る

2018年4月 - 2022年3月

課題番号：18K03657

配分額：4030000円 （ 直接経費：3100000円 、 間接経費：930000円 ）

本研究の目的は弦理論におけるカラビ・ヤウ多様体の幾何学と量子可積分系・2次元電子系におけるスペクトル理論を結びつけ、弦理論の非摂動的側面の理解を深めることである。本年度は当初の研究計画にはなかったが、ブラックホールの準固有振動モードに関する研究を主に行った。これは思いがけず本研究課題に非常に近いことが判明したためである。具体的には以下の2点に関する研究を行った。
<BR>
ブラックホールの摂動論を考えると、2階の線形微分方程式が得られる。この固有方程式に適切な境界条件を課すと、固有値として離散的な複素数のみ許される。このような複素固有値は準固有振動数と呼ばれ、連星ブラックホールの合体の最終段階で重要な役割を果たす。観測との比較のためにも準固有振動数の計算は重要な課題である。本年度の研究では量子力学の摂動論に基づき、準固有振動数を効率よく計算するためのアルゴリズムを提唱した。摂動論は適用範囲が広く、様々なシチュエーションに応用できるのが利点である。ここで提唱したアルゴリズムも幅広いブラックホール時空に対して適用可能なので今後様々な応用が期待できる。
<BR>
これと並行して弦理論におけるトーリック・カラビ・ヤウ多様体と2次元格子上のブロッホ電子模型の対応について考えた。今年度は蜂の巣格子模型に対応するカラビ・ヤウ多様体を探索し、紆余曲折を経て対応物を同定した。その結果、エネルギーバンド幅に対して、弱磁場極限下における解析的な結果を得ることに成功した。まもなく査読論文雑誌JHEPに掲載予定である。

• ホログラフィック双対性で迫るゲージ理論の強結合ダイナミクス

日本学術振興会  科学研究費助成事業 特別研究員奨励費

初田 泰之

詳細を見る

2012年 - 2014年3月

課題番号：12J09542

配分額：2200000円 （ 直接経費：2200000円 ）

ABJM理論の分配関数が受ける非摂動的補正について詳しく調べた。このような非摂動的補正は、世界面インスタントン、D2-インスタントンと呼ばれる2種類のインスタントンによって引き起こされる。昨年度の研究で、世界面インスタントンの補正の一般的な表式は、位相的弦理論の結果から得られることが分かっていた。またD2-インスタントンの低次の補正は、我々が昨年度発見した「極の相殺機構」により、決定できる。本年度はこれら2種類のインスタントンが束縛状態をなす場合の補正を、同様の「極の相殺機構」を用いて決定した。興味深いことに「極の相殺機構」といくつかのインプット・データを考慮してやると、インスタントン束縛状態の非摂動的補正の一般形を予想することが出来、結果は非常にシンプルな形式にまとまった。このことは、ABJM理論の背後に美しい数理的構造が潜んでいることを示唆しており、今後の研究課題である。
またその後の研究により、D2-インスタントンの一般的補正は、リファインされた位相的弦理論により計算出来ることが分かった。また、分配関数だけでなく、1/2 BPS Wilsonループについても同様の解析が可能であることも分かった(両者ともプレプリントサーバー : arXivには既に投稿済、近日中に学術誌に出版予定である)。

• 行列模型を用いたゲージ理論と超弦理論の双対性の研究

日本学術振興会  科学研究費助成事業 特別研究員奨励費

初田 泰之

詳細を見る

2008年 - 2009年

課題番号：08J10894

配分額：1200000円 （ 直接経費：1200000円 ）