arXiv subjects

Goro Ishiki

Publications and source records attributed to Goro Ishiki.

At least 37 records · Page 2Linked to original sources

arXiv2016

Precision lattice test of the gauge/gravity duality at large-$N$

We pioneer a systematic, large-scale lattice simulation of D0-brane quantum mechanics. The large-$N$ and continuum limits of the gauge theory are taken for the first time at various temperatures $0.4 \leq T \leq 1.0$. As a way to directly test the gauge/gravity duality conjecture we compute the internal energy of the black hole directly from the gauge theory and reproduce the coefficient of the supergravity result $E/N^2=7.41T^{14/5}$. This is the first confirmation of the supergravity prediction for the internal energy of a black hole at finite temperature coming directly from the dual gauge theory. We also constrain stringy corrections to the internal energy.

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arXiv2016

Numerical tests of the gauge/gravity duality conjecture for D0-branes at finite temperature and finite N

According to the gauge/gravity duality conjecture, the thermodynamics of gauge theory describing D-branes corresponds to that of black branes in superstring theory. We test this conjecture directly in the case of D0-branes by applying Monte Carlo methods to the corresponding gauge theory, which takes the form of the BFSS matrix quantum mechanics. In particular, we take the continuum limit by extrapolating the UV cutoff to infinity. First we perform simulations at large N so that string loop corrections can be neglected on the gravity side. Our results for the internal energy exhibit the temperature dependence consistent with the prediction including the α' corrections. Next we perform simulations at small N but at lower temperature so that the α' corrections can be neglected on the gravity side. Our results are consistent with the prediction including the leading string loop correction, which suggests that the conjecture holds even at finite N.

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arXiv2016

Kähler structure in the commutative limit of matrix geometry

We consider the commutative limit of matrix geometry described by a large-$N$ sequence of some Hermitian matrices. Under some assumptions, we show that the commutative geometry possesses a Kähler structure. We find an explicit relation between the Kähler structure and the matrix configurations which define the matrix geometry. We also find a relation between the matrix configurations and those obtained from the geometric quantization.

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arXiv2015

Matrix Geometry and Coherent States

We propose a novel method of finding the classical limit of the matrix geometry. We define coherent states for a general matrix geometry described by a large-N sequence of D Hermitian matrices X_μ(μ=1,2, ..., D) and construct a corresponding classical space as a set of all coherent states. We also express various geometric objects on the classical space such as the metric, Levi-Civita connection, curvature and Poisson tensor, in terms of the matrix elements. This method provides a new class of observables in matrix models, which characterize geometric properties of matrix configurations.

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arXiv2014

Emergent bubbling geometries in gauge theories with SU(2|4) symmetry

We study the gauge/gravity duality between bubbling geometries in type IIA supergravity and gauge theories with SU(2|4) symmetry, which consist of N=4 super Yang-Mills on $R\times S^3/Z_k$, N=8 super Yang-Mills on $R\times S^2$ and the plane wave matrix model. We show that the geometries are realized as field configurations in the strong coupling region of the gauge theories. On the gravity side, the bubbling geometries can be mapped to electrostatic systems with conducting disks. We derive integral equations which determine the charge densities on the disks. On the gauge theory side, we obtain a matrix integral by applying the localization to a 1/4-BPS sector of the gauge theories. The eigenvalue densities of the matrix integral turn out to satisfy the same integral equations as the charge densities on the gravity side. Thus we find that these two objects are equivalent.

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arXiv2014

Emergent bubbling geometries in the plane wave matrix model

The gravity dual geometry of the plane wave matrix model is given by the bubbling geometry in the type IIA supergravity, which is described by an axially symmetric electrostatic system. We study a quarter BPS sector of the plane wave matrix model in terms of the localization method and show that this sector can be mapped to a one-dimensional interacting Fermi gas system. We find that the mean-field density of the Fermi gas can be identified with the charge density in the electrostatic system in the gravity side. We also find that the scaling limits in which the dual geometry reduces to the D2-brane or NS5-brane geometry are given as the free limit or the strongly coupled limit of the Fermi gas system, respectively. We reproduce the radii of $S^5$'s in these geometries by solving the Fermi gas model in the corresponding limits.

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arXiv2013

Direct test of the AdS/CFT correspondence by Monte Carlo studies of N=4 super Yang-Mills theory

We perform nonperturbative studies of N=4 super Yang-Mills theory by Monte Carlo simulation. In particular, we calculate the correlation functions of chiral primary operators to test the AdS/CFT correspondence. Our results agree with the predictions obtained from the AdS side that the SUSY non-renormalization property is obeyed by the three-point functions but \emph{not} by the four-point functions investigated in this paper. Instead of the lattice regularization, we use a novel regularization of the theory based on an equivalence in the large-N limit between the N=4 SU(N) theory on RxS^3 and a one-dimensional SU(N) gauge theory known as the plane-wave (BMN) matrix model. The equivalence extends the idea of large-N reduction to a curved space and, at the same time, overcomes the obstacle related to the center symmetry breaking. The adopted regularization preserves 16 SUSY, which is crucial in testing the AdS/CFT correspondence with the available computer resources. The only SUSY breaking effects, which come from the momentum cutoff $Λ$ in R direction, are made negligible by using sufficiently large $Λ$.

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arXiv2013

Holographic description of quantum black hole on a computer

The discovery of the fact that black holes radiate particles and eventually evaporate led Hawking to pose the well-known information loss paradox. This paradox caused a long and serious debate since it claims that the fundamental laws of quantum mechanics may be violated. A possible cure appeared recently from superstring theory, a consistent theory of quantum gravity: if the holographic description of a quantum black hole based on the gauge/gravity duality is correct, the information is not lost and quantum mechanics remains valid. Here we test this gauge/gravity duality on a computer at the level of quantum gravity for the first time. The black hole mass obtained by Monte Carlo simulation of the dual gauge theory reproduces precisely the quantum gravity effects in an evaporating black hole. This result opens up totally new perspectives towards quantum gravity since one can simulate quantum black holes through dual gauge theories.

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arXiv2012

Exact results for perturbative partition functions of theories with SU(2|4) symmetry

In this paper, we study the theories with SU(2|4) symmetry which consist of the plane wave matrix model (PWMM), super Yang-Mills theory (SYM) on RxS^2 and SYM on RxS^3/Z_k. The last two theories can be realized as theories around particular vacua in PWMM, through the commutative limit of fuzzy sphere and Taylor's T-duality. We apply the localization method to PWMM to reduce the partition function and the expectation values of a class of supersymmetric operators to matrix integrals. By taking the commutative limit and performing the T-duality, we also obtain the matrix integrals for SYM on RxS^2 and SYM on RxS^3/Z_k. In this calculation, we ignore possible instanton effects and our matrix integrals describe the perturbative part exactly. In terms of the matrix integrals, we also provide a nonperturbative proof of the large-N reduction for circular Wilson loop operator and free energy in N=4 SYM on RxS^3.

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arXiv2012

Large-N reduction for N=2 quiver Chern-Simons theories on S^3 and localization in matrix models

We study reduced matrix models obtained by the dimensional reduction of N=2 quiver Chern-Simons theories on S^3 to zero dimension and show that if a reduced model is expanded around a particular multiple fuzzy sphere background, it becomes equivalent to the original theory on S^3 in the large-N limit. This is regarded as a novel large-N reduction on a curved space S^3. We perform the localization method to the reduced model and compute the free energy and the vacuum expectation value of a BPS Wilson loop operator. In the large-N limit, we find an exact agreement between these results and those in the original theory on S^3.

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arXiv2011

Testing the AdS/CFT correspondence by Monte Carlo calculation of BPS and non-BPS Wilson loops in 4d N=4 super-Yang-Mills theory

We test the AdS/CFT correspondence by calculating Wilson loops in N = 4 super Yang-Mills theory on R*S^3 in the planar limit. Our method is based on a novel large-N reduction, which reduces the problem to Monte Carlo calculations in the plane-wave matrix model or the BMN matrix model, which is a 1d gauge theory with 16 supercharges. By using the gauge-fixed momentumspace simulation, we obtain results respecting 16 supersymmetries. We report on the Monte Carlo results for the BPS circular Wilson loop, which reproduce the exact result up to strong coupling. As a future prospect, we calculate a track-shapedWilson loop from the gravity side, which shows that a clear test of the AdS/CFT for the non-BPS case is also feasible.

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arXiv2011

Bulk-boundary correlators in the hermitian matrix model and minimal Liouville gravity

We construct the one matrix model (MM) correlators corresponding to the general bulk-boundary correlation numbers of the minimal Liouville gravity (LG) on the disc. To find agreement between both discrete and continuous approach, we investigate the resonance transformation mixing boundary and bulk couplings. It leads to consider two sectors, depending on whether the matter part of the LG correlator is vanishing due to the fusion rules. In the vanishing case, we determine the explicit transformation of the boundary couplings at the first order in bulk couplings. In the non-vanishing case, no bulk-boundary resonance is involved and only the first order of pure boundary resonances have to be considered. Those are encoded in the matrix polynomials determined in our previous paper. We checked the agreement for the bulk-boundary correlators of MM and LG in several non-trivial cases. In this process, we developed an alternative method to derive the boundary resonance encoding polynomials.

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arXiv2011

A non-perturbative formulation of N=4 super Yang-Mills theory based on the large-N reduction

We study a non-perturbative formulation of N=4 super Yang-Mills theory (SYM) on RxS^3 proposed in arXiv:0807.2352. This formulation is based on the large-N reduction, and the theory can be described as a particular large-N limit of the plane wave matrix model (PWMM), which is obtained by dimensionally reducing the original theory over S^3. In this paper, we perform some tests for this proposal. We construct an operator in the PWMM that corresponds to the Wilson loop in SYM in the continuum limit and calculate the vacuum expectation value of the operator for the case of the circular contour. We find that our result indeed agrees with the well-known result first obtained by Erickson, Semenoff and Zarembo. We also compute the beta function at the 1-loop level based on this formulation and see that it is indeed vanishing.

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arXiv2010

Boundary operators in the one-matrix model

The one matrix model is known to reproduce in the continuum limit the (2,2p+1) minimal Liouville gravity. Recently, two of the authors have shown how to construct arbitrary critical boundary conditions within this matrix model. So far, between two such boundary conditions only one boundary operator was constructed. In this paper, we explain how to construct all the set of boundary operators that can be inserted. As a consistency check, we reproduce the corresponding Liouville boundary 2pt function from the matrix model correlator. In addition, we remark a connection between a matrix model relation and the boundary ground ring operator insertion in the continuum theory.

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arXiv2010

Boundary operators in minimal Liouville gravity and matrix models

We interpret the matrix boundaries of the one matrix model (1MM) recently constructed by two of the authors as an outcome of a relation among FZZT branes. In the double scaling limit, the 1MM is described by the (2,2p+1) minimal Liouville gravity. These matrix operators are shown to create a boundary with matter boundary conditions given by the Cardy states. We also demonstrate a recursion relation among the matrix disc correlator with two different boundaries. This construction is then extended to the two matrix model and the disc correlator with two boundaries is compared with the Liouville boundary two point functions. In addition, the realization within the matrix model of several symmetries among FZZT branes is discussed.

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arXiv2010

Supersymmetry non-renormalization theorem from a computer and the AdS/CFT correspondence

We perform Monte Carlo calculation of correlation functions in 4d N=4 super Yang-Mills theory on R*S^3 in the planar limit. In order to circumvent the well-known problem of lattice SUSY, we adopt the idea of a novel large-N reduction, which reduces the calculation to that of corresponding correlation functions in the plane-wave matrix model or the BMN matrix model. This model is a 1d gauge theory with 16 supersymmetries, which can be simulated in a manner similar to the recent studies of the D0-brane system. We study two-point and three-point functions of chiral primary operators at various coupling constant, and find that they agree with the free theory results up to overall constant factors. The ratio of the overall factors for two-point and three-point functions agrees with the prediction of the AdS/CFT correspondence.

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arXiv2010

Boundary correlation numbers in one matrix model

We introduce one matrix model coupled to multi-flavor vectors. The two-flavor vector model is demonstrated to reproduce the two-point correlation numbers of boundary primary fields of two dimensional (2, 2p+1) minimal Liouville gravity on disk, generalizing the loop operator (resolvent) description. The model can properly describe non-trivial boundary conditions for the matter Cardy state as well as for the Liouville field. From this we propose that the n-flavor vector model will be suited for producing the boundary correlation numbers with n different boundary conditions on disk.

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arXiv2010

A Novel Large-N Reduction on S^3: Demonstration in Chern-Simons Theory

We show that the planar Chern-Simons (CS) theory on S^3 can be described by its dimensionally reduced model. This description of CS theory can be regarded as a novel large-N reduction for gauge theories on S^3. We find that if one expands the reduced model around a particular background consisting of multiple fuzzy spheres, the reduced model becomes equivalent to CS theory on S^3 in the planar limit. In fact, we show that the free energy and the vacuum expectation value of unknot Wilson loop in CS theory are reproduced by the reduced model in the large-N limit.

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