arXiv subjects

Masanori Hanada

Publications and source records attributed to Masanori Hanada.

At least 109 records · Page 6Linked to original sources

arXiv2011

A proposal of a fine tuning free formulation of 4d N=4 super Yang-Mills

Recently, a nonperturbative formulation of 4d N=4 super Yang-Mills theory which does not require fine tuning at least to all order in perturbation theory has been proposed by combining two-dimensional lattice and matrix model techniques. In this paper we provide an analogous model by utilizing deconstruction approach of Kaplan et al. Two-dimensional lattice with a plane wave deformation is deconstructed from a matrix model and two additional dimensions emerge through the Myers effect. In other words we construct a D1-brane theory from which a D3-brane theory comes out. The action is much simpler than the previous formulation and hence numerical study, which enables us to test the AdS/CFT duality at fully nonperturbative level, becomes much easier.

hep-lat↗

arXiv2011

Generating new dualities through the orbifold equivalence: a demonstration in ABJM and four-dimensional quivers

We show that the recently proposed large $N$ equivalence between ABJM theories with Chern-Simons terms of different rank and level, U(N_1)_{k_1}\times U(N_1)_{-k_1} and U(N_2)_{k_2}\times U(N_2)_{-k_2}, but the same value of N' =N_1 k_1=N_2 k_2, can be explained using planar equivalence in the mirror duals. The combination of S-dualities and orbifold equivalence can be applied to other cases as well, with very appealing results. As an example we show that two different quiver theories with k nodes can be easily shown to be Seiberg dual through the orbifold equivalence, but it requires order k^2 steps to give a proof when Seiberg duality is performed node by node.

hep-th↗

arXiv2011

Large-Nc universality of phases in QCD and QCD-like theories

QCD with a finite baryon chemical potential, despite its importance, is not well understood because the standard lattice QCD simulation is not applicable due to the sign problem. Although sign-free QCD-like theories have been studied intensively, relation to QCD with a finite baryon chemical potential was not clear until recently. In this talk we explain the large-Nc equivalences between QCD and various QCD-like theories, which lead us to a unified viewpoint for QCD with baryon and isospin chemical potentials, SO(2Nc) and Sp(2Nc) gauge theories. In particular two-flavor QCD with the baryon chemical potential is equivalent to its phase quenched version in a certain parameter region, which is relevant for heavy ion collision experiments.

hep-ph↗

arXiv2011

Direct test of the gauge-gravity correspondence for Matrix theory correlation functions

We study correlation functions in (0+1)-dimensional maximally supersymmetric U(N) Yang-Mills theory, which was proposed by Banks et al. as a non-perturbative definition of 11-dimensional M-theory in the infinite-momentum frame. We perform first-principle calculations using Monte Carlo simulations, and compare the results against the predictions obtained previously based on the gauge-gravity correspondence from 10 dimensions. After providing a self-contained review on these predictions, we present clear evidence that the predictions in the large-N limit actually hold even at small N such as N=2 and 3. The predicted behavior seems to continue to the far infrared regime, which goes beyond the naive range of validity of the 10D supergravity analysis. This suggests that the correlation functions also contain important information on the M-theory limit.

hep-th↗

arXiv2011

Two-dimensional lattice for four-dimensional N=4 supersymmetric Yang-Mills

We construct a lattice formulation of a mass-deformed two-dimensional N=(8,8) super Yang-Mills theory with preserving two supercharges exactly. Gauge fields are represented by compact unitary link variables, and the exact supercharges on the lattice are nilpotent up to gauge transformations and SU(2)_R rotations. Due to the mass deformation, the lattice model is free from the vacuum degeneracy problem, which was encountered in earlier approaches, and flat directions of scalar fields are stabilized giving discrete minima representing fuzzy S^2. Around the trivial minimum, quantum continuum theory is obtained with no tuning, which serves a nonperturbative construction of the IIA matrix string theory. Moreover, around the minimum of k-coincident fuzzy spheres, four-dimensional N=4 U(k) super Yang-Mills theory with two commutative and two noncommutative directions emerges. In this theory, sixteen supersymmetries are broken by the mass deformation to two. Assuming the breaking is soft, we give a scenario leading to undeformed N=4 super Yang-Mills on R^4 without any fine tuning. As an evidence for the validity of the assumption, some computation of 1-loop radiative corrections is presented.

hep-lat↗

arXiv2011

Orbifold equivalence and the sign problem at finite baryon density

We point out that SO(2N_{c}) gauge theory with N_{f} fundamental Dirac fermions does not have a sign problem at finite baryon number chemical potential μ_{B}. One can thus use lattice Monte Carlo simulations to study this theory at finite density. The absence of a sign problem in the SO(2N_{c}) theory is particularly interesting because a wide class of observables in the SO(2N_{c}) theory coincide with observables in QCD in the large N_{c} limit, as we show using the technique of large N_{c} orbifold equivalence. We argue that the orbifold equivalence between the two theories continues to hold at μ_{B} \neq 0 provided one adds appropriate deformation terms to the SO(2N_{c}) theory. This opens up the prospect of learning about QCD at μ_{B} \neq 0 using lattice studies of the SO(2N_{c}) theory.

hep-th↗

arXiv2011

Nonperturbative studies of supersymmetric matrix quantum mechanics with 4 and 8 supercharges at finite temperature

We investigate thermodynamic properties of one-dimensional U(N) supersymmetric gauge theories with 4 and 8 supercharges in the planar large-N limit by Monte Carlo calculations. Unlike the 16 supercharge case, the threshold bound state with zero energy is widely believed not to exist in these models. This led A.V. Smilga to conjecture that the internal energy decreases exponentially at low temperature instead of decreasing with a power law. In the 16 supercharge case, the latter behavior was predicted from the dual black 0-brane geometry and confirmed recently by Monte Carlo calculations. Our results for the models with 4 and 8 supercharges indeed support the exponential behavior, revealing a qualitative difference from the 16 supercharge case.

hep-th↗

arXiv2011

Absence of sign problem in two-dimensional N=(2,2) super Yang-Mills on lattice

We show that N=(2,2) SU(N) super Yang-Mills theory on lattice does not have sign problem in the continuum limit, that is, under the phase-quenched simulation phase of the determinant localizes to 1 and hence the phase-quench approximation becomes exact. Among several formulations, we study models by Cohen-Kaplan-Katz-Unsal (CKKU) and by Sugino. We confirm that the sign problem is absent in both models and that they converge to the identical continuum limit without fine tuning. We provide a simple explanation why previous works by other authors, which claim an existence of the sign problem, do not capture the continuum physics.

hep-lat↗

arXiv2010

Large-N reduction in QCD-like theories with massive adjoint fermions

Large-N QCD with heavy adjoint fermions emulates pure Yang-Mills theory at long distances. We study this theory on a four- and three-torus, and analytically argue the existence of a large-small volume equivalence. For any finite mass, center symmetry unbroken phase exists at sufficiently small volume and this phase can be used to study the large-volume limit through the Eguchi-Kawai equivalence. A finite temperature version of volume independence implies that thermodynamics on R^3 x S^1 can be studied via a unitary matrix quantum mechanics on S^1, by varying the temperature. To confirm this non-perturbatively, we numerically study both zero- and one-dimensional theories by using Monte-Carlo simulation. Order of finite-N corrections turns out to be 1/N. We introduce various twisted versions of the reduced QCD which systematically suppress finite-N corrections. Using a twisted model, we observe the confinement/deconfinement transition on a 1^3 x 2-lattice. The result agrees with large volume simulations of Yang-Mills theory. We also comment that the twisted model can serve as a non-perturbative formulation of the non-commutative Yang-Mills theory.

hep-th↗

arXiv2010

Numerical approach to SUSY quantum mechanics and the gauge/gravity duality

We demonstrate that Monte-Carlo simulation is a practical tool to study nonperturbative aspects of supersymmetric quantum mechanics. As an example we study D0-brane quantum mechanics in the context of superstring theory. Numerical data nicely reproduce predictions from gravity side, including the coupling constant dependence of the string alpha' correction. This strongly suggests the duality to hold beyond the supergravity approximation. Although detail of the stringy correction cannot be obtained by state-of-the-art techniques in gravity side, in the matrix quantum mechanics we can obtain concrete values. Therefore the Monte-Carlo simulation combined with the duality provides a powerful tool to study the superstring theory.

hep-th↗

arXiv2009

Four-dimensional N=1 super Yang-Mills from matrix model

We consider a supersymmetric matrix quantum mechanics. This is obtained by adding Myers and mass terms to the dimensional reduction of 4d N=1 super Yang-Mills theory to one dimension. Using this model we construct 4d N=1 super Yang-Mills theory in the planar limit by using the Eguchi-Kawai equivalence. The same matrix quantum mechanics is also used to provide a nonperturbative formulation of 4d N=1 super Yang-Mills theory on noncommutative space.

hep-th↗

arXiv2009

Monte Carlo studies of Matrix theory correlation functions

We study correlation functions in (0+1)-dimensional maximally supersymmetric U(N) gauge theory, which represents the low-energy effective theory of D0-branes. In the large-N limit, the gauge-gravity duality predicts power-law behaviors in the infrared region for the two-point correlation functions of operators corresponding to supergravity modes. We evaluate such correlation functions on the gauge theory side by the Monte Carlo method. Clear power-law behaviors are observed at N=3, and the predicted exponents are confirmed consistently. Our results suggest that the agreement extends to the M-theory regime, where the supergravity analysis in 10 dimensions may not be justified a priori.

hep-th↗

arXiv2009

Large-N reduced models of supersymmetric quiver, Chern-Simons gauge theories and ABJM

Using the Eguchi-Kawai equivalence, we provide regularizations of supersymmetric quiver and Chern-Simons gauge theories which leave the supersymmetries unbroken. This allow us to study many interesting theories on a computer. As examples we construct large-$N$ reduced models of supersymmetric QCD with flavor and the ABJM model of multiple M2 branes.

hep-th↗

arXiv2009

Lattice study of two-dimensional N=(2,2) super Yang-Mills at large-N

We study two-dimensional N=(2,2) SU(N) super Yang-Mills theory on Euclidean two-torus using Sugino's lattice regularization. We perform the Monte-Carlo simulation for N=2,3,4,5 and then extrapolate the result to N = infinity. With the periodic boundary conditions for the fermions along both circles, we establish the existence of a bound state in which scalar fields clump around the origin, in spite of the existence of a classical flat direction. In this phase the global (Z_N)^2 symmetry turns out to be broken. We provide a simple explanation for this fact and discuss its physical implications.

hep-lat↗

arXiv2009

Higher derivative corrections to black hole thermodynamics from supersymmetric matrix quantum mechanics

We perform a direct test of the gauge-gravity duality associated with the system of N D0-branes in type IIA superstring theory at finite temperature. Based on the fact that higher derivative corrections to the type IIA supergravity action start at the order of α'^3, we derive the internal energy in expansion around infinite 't Hooft coupling up to the subleading term with one unknown coefficient. The power of the subleading term is shown to be nicely reproduced by the Monte Carlo data obtained nonperturbatively on the gauge theory side at finite but large effective (dimensionless) 't Hooft coupling constant. This suggests, in particular, that the open strings attached to the D0-branes provide the microscopic origin of the black hole thermodynamics of the dual geometry including α' corrections. The coefficient of the subleading term extracted from the fit to the Monte Carlo data provides a prediction for the gravity side, which can be checked once the complete form of the O(α'^3) corrections to the supergravity action is obtained.

hep-th↗

arXiv2009

On the shape of a D-brane bound state and its topology change

As is well known, coordinates of D-branes are described by NxN matrices. From generic non-commuting matrices, it is difficult to extract physics, for example, the shape of the distribution of positions of D-branes. To overcome this problem, we generalize and elaborate on a simple prescription, first introduced by Hotta, Nishimura and Tsuchiya, which determines the most appropriate gauge to make the separation between diagonal components (D-brane positions) and off-diagonal components. This prescription makes it possible to extract the distribution of D-branes directly from matrices. We verify the power of it by applying it to Monte-Carlo simulations for various lower dimensional Yang-Mills matrix models. In particular, we detect the topology change of the D-brane bound state for a phase transition of a matrix model; the existence of this phase transition is expected from the gauge/gravity duality, and the pattern of the topology change is strikingly similar to the counterpart in the gravity side, the black hole/black string transition. We also propose a criterion, based on the behavior of the off-diagonal components, which determines when our prescription gives a sensible definition of D-brane positions. We provide numerical evidence that our criterion is satisfied for the typical distance between D-branes. For a supersymmetric model, positions of D-branes can be defined even at a shorter distance scale. The behavior of off-diagonal elements found in this analysis gives some support for previous studies of D-brane bound states.

hep-th↗

arXiv2008

Worldsheet Analysis of Gauge/Gravity Dualities

Gauge/gravity dualities are investigated from the worldsheet point of view. In [arXiv:0706.1163] and [arXiv:0708.2463], a duality between 4d SYM and supergravity on AdS_5xS^5 has been partly explained by using an anisotropic scale invariance of worldsheet theory. In this paper, we refine the argument and generalize it to lower dimensional cases. We show the correspondence between the Wilson loops in (p+1)-d SYM and the minimal surface in the black p-brane background. Although the scale invariance does not exist in these cases, the generalized scale transformation can be utilized. We also find that the energy density of open strings can be related to the ADM mass of the p-brane without relying on this symmetry.

hep-th↗

arXiv2008

On Matrix Model Formulations of Noncommutative Yang-Mills Theories

We study stability of noncommutative spaces in matrix models and discuss the continuum limit which leads to noncommutative Yang-Mills theories (NCYM). It turns out that most of noncommutative spaces in bosonic models are unstable. This indicates perturbative instability of fuzzy R^D pointed out by Van Raamsdonk and Armoni et al. persists to nonperturbative level in these cases. In this sense, these bosonic NCYM are not well-defined, or at least their matrix model formulations studied in this paper do not work. We also show that noncommutative backgrounds are stable in a supersymmetric matrix model deformed by a cubic Myers term, though the deformation itself breaks supersymmetry.

hep-th↗