arXiv subjects

Goro Ishiki

Publications and source records attributed to Goro Ishiki.

At least 19 recordsLinked to original sources

arXiv2026

Localization of the BFSS matrix model and three-point amplitude in M-theory

We apply the localization method to the BFSS matrix model with a particular class of boundary conditions, that is related to a scattering problem of 11-dimensional M-theory. For the boundary condition that corresponds to the three-point amplitude of gravitons, we exactly compute the partition function of the model based on the localization method. We find that the result correctly reproduces the expected momentum dependence of the three point amplitude.

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arXiv2026

Derivation of the NS5-brane limit of the plane wave matrix model

From the gauge/gravity duality, it was predicted that there exists a nontrivial double scaling limit of the plane wave matrix model (the BMN matrix model), which describes the type IIA little string theory (LST) on $R\times S^5$. We show on the gauge theory side that such a limit indeed exists for the partition function and in a certain 1/4 BPS sector of the matrix model, and consequently derive an eigenvalue integral, which is expected to describe the 1/4 BPS sector of LST.

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arXiv2025

Classical BPS M5-brane on the plane wave background

We consider the bosonic theory for a single M5-brane on the plane-wave background and derive a family of BPS solutions with non-zero components of the angular momentum. By explicit construction of a BPS solution, we find the solution describes an ellipsoidal five-brane rotating without changing its shape. The methodology developed in this paper is expected to provide a strategy for obtaining the BPS solutions that correspond to a BPS sector in the dual gauge theory, such as the BMN matrix model.

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arXiv2024

Matrix regularization for gauge theories

We consider how gauge theories can be described by matrix models. Conventional matrix regularization is defined for scalar functions and is not applicable to gauge fields, which are connections of fiber bundles. We clarify how the degrees of freedom of gauge fields are related to the matrix degrees of freedom, by formulating the Seiberg-Witten map between them.

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arXiv2023

On the existence of the NS5-brane limit of the plane wave matrix model

We consider a double scaling limit of the plane wave matrix model (PWMM), in which the gravity dual geometry of PWMM reduces to a class of spherical NS5-brane solutions. We identify the form of the scaling limit for the dual geometry of PWMM around a general vacuum and then translate the limit into the field theoretic language. We also show that the limit indeed exists at least in a certain planar 1/4-BPS sector of PWMM by using the localization computation analytically. In addition, we employ the hybrid Monte Carlo method to compute the matrix integral obtained by the localization method, near the parameter region where the supergravity approximation is valid. Our numerical results, which are considered to be the first computation of quantum loop correction to the Lin-Maldacena geometry, suggest that the double scaling limit exists beyond the planar sector.

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arXiv2023

Vector bundles on fuzzy Kähler manifolds

We propose a matrix regularization of vector bundles over a general closed Kähler manifold. This matrix regularization is given as a natural generalization of the Berezin-Toeplitz quantization and gives a map from sections of a vector bundle to matrices. We examine the asymptotic behaviors of the map in the large-$N$ limit. For vector bundles with algebraic structure, we derive a beautiful correspondence of the algebra of sections and the algebra of corresponding matrices in the large-$N$ limit. We give two explicit examples for monopole bundles over a complex projective space $CP^n$ and a torus $T^{2n}$.

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arXiv2022

Matrix regularization for tensor fields

We propose a novel matrix regularization for tensor fields. In this regularization, tensor fields are described as rectangular matrices and both area-preserving diffeomorphisms and local rotations of the orthonormal frame are realized as unitary similarity transformations of matrices in a unified way. We also show that the matrix commutator corresponds to the covariantized Poisson bracket for tensor fields in the large-$N$ limit.

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arXiv2021

Laplacians on Fuzzy Riemann Surfaces

We consider the matrix regularization of scalar fields on a Riemann surface with a general gauge-field background. We propose a construction of the fuzzy version of the Laplacian.

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arXiv2020

The matrix regularization for Riemann surfaces with magnetic fluxes

We consider the matrix regularization of fields on a Riemann surface which couple to gauge fields with a nonvanishing magnetic flux. We show that such fields are described as rectangular matrices in the matrix regularization. We construct the matrix regularization explicitly for the case of the sphere and torus based on the Berezin-Toeplitz quantization, and also discuss a possible generalization to cases with higher genera. We also discuss the matrix version of the Laplacian acting on the rectangular matrices.

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arXiv2019

Partial deconfinement in gauge theories

We provide the evidence for the existence of partially deconfined phase in large-$N$ gauge theory. In this phase, the SU($M$) subgroup of SU($N$) gauge group deconfines, where $\frac{M}{N}$ changes continuously from zero (confined phase) to one (deconfined phase). The partially deconfined phase may exist in real QCD with $N=3$.

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arXiv2019

Diffeomorphisms on Fuzzy Sphere

Diffeomorphisms can be seen as automorphisms of the algebra of functions. In the matrix regularization, functions on a smooth compact manifold are mapped to finite size matrices. We consider how diffeomorphisms act on the configuration space of the matrices through the matrix regularization. For the case of the fuzzy $S^2$, we construct the matrix regularization in terms of the Berezin-Toeplitz quantization. By using this quantization map, we define diffeomorphisms on the space of matrices. We explicitly construct the matrix version of holomorphic diffeomorphisms on $S^2$. We also propose three methods of constructing approximate invariants on the fuzzy $S^2$. These invariants are exactly invariant under area-preserving diffeomorphisms and only approximately invariant (i.e. invariant in the large-$N$ limit) under the general diffeomorphisms.

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arXiv2019

The null identities for boundary operators in the $(2,2p+1)$ minimal gravity

By using the matrix-model representation, we show that correlation numbers of boundary changing operators (BCO) in $(2,2p+1)$ minimal Liouville gravity satisfy some identities, which we call the null identities. These identities enable us to express the correlation numbers of BCO in terms of those of boundary preserving operators. We also discuss a physical implication of the null identities as the manifestation of the boundary interaction.

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arXiv2019

Partial Deconfinement

We argue that the confined and deconfined phases in gauge theories are connected by a partially deconfined phase (i.e. SU(M) in SU(N), where M<N, is deconfined), which can be stable or unstable depending on the details of the theory. When this phase is unstable, it is the gauge theory counterpart of the small black hole phase in the dual string theory. Partial deconfinement is closely related to the Gross-Witten-Wadia transition, and is likely to be relevant to the QCD phase transition. The mechanism of partial deconfinement is related to a generic property of a class of systems. As an instructive example, we demonstrate the similarity between the Yang-Mills theory/string theory and a mathematical model of the collective behavior of ants [Beekman et al., Proceedings of the National Academy of Sciences, 2001]. By identifying the D-brane, open string and black hole with the ant, pheromone and ant trail, the dynamics of two systems closely resemble with each other, and qualitatively the same phase structures are obtained.

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arXiv2018

Information metric, Berry connection and Berezin-Toeplitz quantization for matrix geometry

We consider the information metric and Berry connection in the context of noncommutative matrix geometry. We propose that these objects give a new method of characterizing the fuzzy geometry of matrices. We first give formal definitions of these geometric objects and then explicitly calculate them for the well-known matrix configurations of fuzzy $S^2$ and fuzzy $S^4$. We find that the information metrics are given by the usual round metrics for both examples, while the Berry connections coincide with the configurations of the Wu-Yang monopole and the Yang monopole for fuzzy $S^2$ and fuzzy $S^4$, respectively. Then, we demonstrate that the matrix configurations of fuzzy $S^n$ $(n=2,4)$ can be understood as images of the embedding functions $S^n\rightarrow \textbf{R}^{n+1}$ under the Berezin-Toeplitz quantization map. Based on this result, we also obtain a mapping rule for the Laplacian on fuzzy $S^4$.

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arXiv2018

Commutative Geometry for Non-commutative D-branes by Tachyon Condensation

There is a difficulty in defining the positions of the D-branes when the scalar fields on them are non-abelian. We show that we can use tachyon condensation to determine the position or the shape of D0-branes uniquely as a commutative region in spacetime together with non-trivial gauge flux on it, even if the scalar fields are non-abelian. We use the idea of the so-called coherent state method developed in the field of matrix models in the context of the tachyon condensation. We investigate configurations of noncommutative D2-brane made out of D0-branes as examples. In particular, we examine a Moyal plane and a fuzzy sphere in detail, and show that whose shapes are commutative $\mathbb{R}^2$ and $S^2$, respectively, equipped with uniform magnetic flux on them. We study the physical meaning of this commutative geometry made out of matrices, and propose an interpretation in terms of K-homology.

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arXiv2017

Spherical transverse M5-branes from the plane wave matrix model

We consider matrix theoretical description of transverse M5-branes in M-theory on the 11-dimensional maximally supersymmetric pp-wave background. We apply the localization to the plane wave matrix model (PWMM) and show that the transverse spherical fivebranes with zero light cone energy in M-theory are realized as the distribution of low energy moduli of the $SO(6)$ scalar fields in PWMM.

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arXiv2017

On the transverse M5-branes in matrix theory

It has been a long-standing problem how the transverse M5-branes are described in the matrix-model formulations of M-theory. We consider this problem for M-theory on the maximally supersymmetric pp-wave geometry, which admits transverse spherical M5-branes with zero light-cone energy. By using the localization, we directly analyze the strong coupling region of the corresponding matrix theory called the plane wave matrix model (PWMM). Under the assumption that the low energy modes of the scalar fields in PWMM become mutually commuting in the strong coupling region, we show that the eigenvalue density of the $SO(6)$ scalars in the low energy region exactly agrees with the shape of the spherical M5-branes in the decoupling limit. This result gives a strong evidence that the transverse M5-branes are indeed contained in the matrix theory and the theory realizes a second quantization of the M-theory.

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arXiv2016

Supergravity from D0-brane Quantum Mechanics

The gauge/gravity duality conjecture claims the equivalence between gauge theory and superstring/M-theory. In particular, the one-dimensional gauge theory of D0-branes and type IIA string theory should agree on properties of hot black holes. Type IIA superstring theory predicts the leading $N^2$ behavior of the black hole internal energy to be $E/N^2=a_0T^{14/5}+ a_1T^{23/5}+a_2T^{29/5}+\cdots$ with the supergravity prediction $a_0=7.41$ and unknown coefficients $a_1$, $a_2$, $\ldots$ associated with stringy corrections. In order to test this duality we perform a lattice study of the gauge theory and extract a continuum, large-$N$ value of $a_0=7.4\pm 0.5$---the first direct confirmation of the supergravity prediction at finite temperature---and constrain the stringy corrections ($a_1=-9.7\pm2.2$ and $a_2=5.6\pm1.8$). We also study the sub-leading $1/N^2$ corrections to the internal energy.

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