arXiv subjects

Yasuyuki Hatsuda

Publications and source records attributed to Yasuyuki Hatsuda.

At least 19 recordsLinked to original sources

arXiv2026

Quarter-indices for basic ortho-symplectic corners

We study supersymmetric quarter-indices for corner configurations in 4d $\mathcal{N}=4$ super Yang-Mills theory with orthogonal and symplectic gauge groups. For the basic Y-junctions, we obtain exact closed-form expressions for the indices by making use of the Gustafson type integral formula and the Higgsing method. We demonstrate the equality of the quarter-indices between dual configurations, providing evidence for S-duality of the corner configurations. In the special fugacity limit, the indices admit an interpretation in terms of the vacuum characters of the W-algebras of type BCD, and the Lie superalgebra $\mathfrak{osp}(1|2N)$ as the corner vertex operator algebras.

hep-th↗

arXiv2026

Tensor Network Formulation of $\mathcal{PT}$-Symmetric Quantum Field Theory

We develop a non-perturbative analytic tensor network formulation of $\mathcal{PT}$-symmetric scalar field theories defined on complex integration contours. Applying this formulation to the two-dimensional $\mathcal{PT}$-symmetric $ϕ^4$ theory at negative quartic coupling, we derive an explicit analytic expression for the initial tensor and show that its components separate into even and odd sectors according to the parity of the sum of the tensor indices. We further formulate the theory on an alternative complex contour and analytically establish, in arbitrary dimensions, an exact finite-volume relation between the lattice partition function defined on this contour and the real part of the analytic continuation of the Hermitian lattice $ϕ^4$ partition function to negative quartic coupling.

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arXiv2026

Exact WKB and Quantum Periods for Extremal Black Hole Quasinormal Modes

We apply exact WKB analysis to the spectral problem arising in black hole perturbation theory. The boundary conditions for quasinormal modes lead to exact quantization conditions for the complex frequencies. To solve these conditions, one needs to evaluate the so-called quantum periods, or Voros symbols. For scalar perturbations of extremal Reissner--Nordström and Kerr black holes, we compute these quantities up to very high orders in the WKB expansion and perform Borel--Padé resummation. The resulting resummed quantization conditions successfully reproduce the correct quasinormal mode frequencies with high precision.

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arXiv2026

Interface line operators in $\mathcal{N}=4$ SYM theories and supersymmetric indices

We study configurations of two $\mathcal{N}=4$ super Yang-Mills theories of unitary gauge groups connected by the BPS interfaces involving line operators. We find strong evidence of S-duality of the configurations as precise matching of the line defect half-indices which enumerate the BPS local operators at the junctions of the interfaces and line operators. The interface line defect half-indices are expressible as intriguing closed-form formulae involving the $q$-binomial coefficients and the principal specializations of the Schur functions.

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arXiv2025

S-duality of boundary lines in $\mathcal{N}=4$ SYM theories and supersymmetric indices

We analyze the supersymmetric defect indices of $\mathcal{N}=4$ super Yang Mills theories which are simultaneously decorated by the BPS line operators and the boundary conditions. We demonstrate that the two-point functions of the boundary 't Hooft lines of magnetic charges associated with the minuscule representations in the presence of the regular Nahm pole boundary conditions can be obtained by applying the Higgsing prescription to the half-indices of the Dirichlet boundary conditions. Accordingly, we find precise matching of the indices for pairs of the S-dual configurations with the Wilson lines and Neumann boundary conditions and those with the 't Hooft lines and the regular Nahm pole boundary conditions. Alternatively, we analytically compute the indices by means of the inner product of the Macdonald polynomials to find the exact closed-form expressions.

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arXiv2025

$\mathcal{N}=4$ line defect correlators of type BCD

We analyze the line defect correlation functions decorating the supersymmetric indices of $\mathcal{N}=4$ super Yang-Mills theories with orthogonal and symplectic gauge groups. We obtain exact closed-form expressions for the correlators by means of combinatorial methods associated with the group characters, including the generalized Murnaghan-Nakayama rules. The exact results for the large $N$ correlators lead to the gravity indices for the gravity dual spectrum of the fluctuations of the fundamental string wrapping $AdS_2$ and those of the fat string, the D5-brane wrapping $AdS_2$ $\times$ $\mathbb{RP}^4$.

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arXiv2025

Non-perturbative effects in JT gravity from KdV equations

It is well-known that the partition function of the Jackiw-Teitelboim (JT) gravity is obtained by an integral transformation of volumes of moduli spaces for Riemann surfaces, also known as the Weil-Petersson volumes. This fact enables us to compute the perturbative genus expansion of the partition function by solving a KdV-type non-linear partial differential equation. In this work, we find that this KdV equation also admits transseries solutions. We give a systematic algorithm to explicitly construct a one-parameter transseries solution to the KdV equation. Our approach is based on general two-dimensional topological gravity, and the results for the JT gravity are easily obtained as a special case. The results in the leading non-perturbative sector perfectly agree with another independent calculation from topological recursions in random matrices.

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arXiv2025

Deformed Schur indices and Macdonald polynomials

The Schur index in four-dimensional $\mathcal{N}=4$ super Yang-Mills theory with $U(N)$ gauge group has a natural two-parameter deformation. We find that a matrix integral in such a deformed Schur index can be exactly evaluated by using Macdonald polynomials. The resulting expression is a simple combinatorial summation over partitions. An extension to line operator indices is straightforward. In particular, for an anti-symmetric representation, the line operator index has a relatively simple form. We further discuss infinite $N$ analysis and finite $N$ giant graviton expansions.

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arXiv2025

Orbifold ETW brane and half-indices

We study the half-indices of $\mathcal{N}=4$ super Yang-Mills theories of orthogonal and symplectic gauge groups. We find precise matching pairs of the half-indices as strong evidence of dualities of the half-BPS boundary conditions and interfaces. The half-indices encode the spectra of excitations on the holographically dual orbifold ETW brane and giant gravitons. The exact form of the index for the orbifold ETW giant gravitons is obtained from the giant graviton expansion of the half-index.

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arXiv2024

Spectral Problems for Quasinormal Modes of Black Holes

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, etc. 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.

gr-qc↗

arXiv2024

Giant graviton expansions and ETW brane

We study the giant gravitons in the $AdS_4$ bagpipe geometries involving end-of-the-world (ETW) brane constructed by a single $5$-brane and either two stacks or one stack of D3-branes in Type IIB string theory. From the exact formulae and giant graviton expansions of the half-indices for the half-BPS boundary conditions and interfaces in $\mathcal{N}=4$ super Yang-Mills theory, we obtain the BPS spectra of the fluctuation modes of the $AdS_4$ bagpipe geometries including the ETW brane region.

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arXiv2024

Perturbative quasinormal mode frequencies

We often encounter a situation that black hole solutions can be regarded as continuous deformations of simpler ones, or modify general relativity by continuous parameters. We develop a general framework to compute high-order perturbative corrections to quasinormal mode frequencies in such deformed problems. Our method has many applications, and allows to compute numerical values of the high-order corrections very accurately. For several examples, we perform this computation explicitly, and discuss analytic properties of the quasinormal mode frequencies for deformation parameters.

gr-qc↗

arXiv2023

Excitations of bubbling geometries for line defects

The half-BPS Wilson line operators in the irreducible representations labeled by the Young diagrams for $\mathcal{N}=4$ $U(N)$ super Yang-Mills theory have gravity dual descriptions. When the number $k$ of boxes of the diagram grows as $k\sim N^2$, the bubbling geometries emerge. We evaluate the spectra of quantum fluctuations on the bubbling geometries from the large $N$ and large $k$ limit of the supersymmetric indices decorated by the Wilson lines. The spectra of excitations over multi-particle $1/8$- and $1/2$-BPS states agree with the numbers of conjugacy classes of general linear group over finite fields while degeneracies of single particle BPS states are given by the general necklace polynomial. The bubbling geometry exhibits a new class of asymptotic degeneracy of states.

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arXiv2023

Large $N$ and large representations of Schur line defect correlators

We study the large $N$ and large representation limits of the Schur line defect correlators of the Wilson line operators transforming in the (anti)symmetric, hook and rectangular representations for $\mathcal{N}=4$ $U(N)$ super Yang-Mills theory. By means of the factorization property, the large $N$ correlators of the Wilson line operators in arbitrary representations can be exactly calculated in principle. In the large representation limit they turn out to be expressible in terms of certain infinite series such as Ramanujan's general theta functions and the $q$-analogues of multiple zeta values ($q$-MZVs). Several generating functions for combinatorial objects, including partitions with non-negative cranks and conjugacy classes of general linear groups over finite fields, emerge from the large $N$ correlators. Also we find conjectured properties of the automorphy and the hook-length expansion satisfied by the large $N$ correlators.

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arXiv2023

Exact $\mathcal{N}=2^{*}$ Schur line defect correlators

We study the Schur line defect correlation functions in $\mathcal{N}=4$ and $\mathcal{N}=2^*$ $U(N)$ super Yang-Mills (SYM) theory. We find exact closed-form formulae of the correlation functions of the Wilson line operators in the fundamental, antisymmetric and symmetric representations via the Fermi-gas method in the canonical and grand canonical ensembles. All the Schur line defect correlators are shown to be expressible in terms of multiple series that generalizes the Kronecker theta function. From the large $N$ correlators we obtain generating functions for the spectra of the D5-brane giant and the D3-brane dual giant and find a correspondence between the fluctuation modes and the plane partition diamonds.

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arXiv2022

Large $N$ expansion of an integrated correlator in $\mathcal{N}=4$ SYM

Recently Dorigoni, Green and Wen conjectured a remarkable exact formula for an integrated correlator of four superconformal primary operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory. In this work, we investigate its large $N$ limit in detail. We show that the formula of Dorigoni, Green and Wen can be recast into the sum over the contributions of $(p,q)$-strings. Due to the $SL(2,\mathbb{Z})$ duality, all the contributions are governed by a single function, typically appearing as the fundamental string contribution. The large order behavior for the perturbative genus expansion of this function allows us to reveal the large $N$ non-perturbative corrections, which we interpret as the D3-brane instantons in the holographically dual type IIB string theory. The same result is obtained more systematically by using a Laplace-difference equation for the integrated correlator.

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arXiv2022

$\mathcal{N}=2^{*}$ Schur indices

We find closed-form expressions for the Schur indices of 4d $\mathcal{N}=2^{*}$ super Yang-Mills theory with unitary gauge groups for arbitrary ranks via the Fermi-gas formulation. They can be written as a sum over the Young diagrams associated with spectral zeta functions of an ideal Fermi-gas system. These functions are expressed in terms of the twisted Weierstrass functions, generating functions for quasi-Jacobi forms. The indices lie in the polynomial ring generated by the Kronecker theta function and the Weierstrass functions which contains the polynomial ring of the quasi-Jacobi forms. The grand canonical ensemble allows for another simple exact form of the indices as infinite series. In addition, we find that the unflavored Schur indices and their limits can be expressed in terms of several generating functions for combinatorial objects, including sum of triangular numbers, generalized sums of divisors and overpartitions.

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arXiv2022

Fermi-gas correlators of ADHM theory and triality symmetry

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 next-to-leading corrections analytically.

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