arXiv subjects

Jun Nishimura

Publications and source records attributed to Jun Nishimura.

At least 109 records · Page 6Linked to original sources

arXiv2011

Towards an Effective Importance Sampling in Monte Carlo Simulations of a System with a Complex Action

The sign problem is a notorious problem, which occurs in Monte Carlo simulations of a system with a partition function whose integrand is not positive. One way to simulate such a system is to use the factorization method where one enforces sampling in the part of the configuration space which gives important contribution to the partition function. This is accomplished by using constraints on some observables chosen appropriately and minimizing the free energy associated with their joint distribution functions. These observables are maximally correlated with the complex phase. Observables not in this set essentially decouple from the phase and can be calculated without the sign problem in the corresponding "microcanonical" ensemble. These ideas are applied on a simple matrix model with very strong sign problem and the results are found to be consistent with analytic calculations using the Gaussian Expansion Method.

hep-lat↗

arXiv2011

Expanding universe as a classical solution in the Lorentzian matrix model for nonperturbative superstring theory

Recently we have shown by Monte Carlo simulation that expanding (3+1)-dimensional universe appears dynamically from a Lorentzian matrix model for type IIB superstring theory in (9+1)-dimensions. The mechanism for the spontaneous breaking of rotational symmetry relies crucially on the noncommutative nature of the space. Here we study the classical equations of motion as a complementary approach. In particular, we find a unique class of SO(3) symmetric solutions, which exhibits the time-dependence compatible with the expanding universe. The space-space noncommutativity is exactly zero, whereas the space-time noncommutativity becomes significant only towards the end of the expansion. We interpret the Monte Carlo results and the classical solution as describing the behavior of the model at earlier time and at later time, respectively.

hep-th↗

arXiv2011

Systematic study of the SO(10) symmetry breaking vacua in the matrix model for type IIB superstrings

We study the properties of the space-time that emerges dynamically from the matrix model for type IIB superstrings in ten dimensions. We calculate the free energy and the extent of space-time using the Gaussian expansion method up to the third order. Unlike previous works, we study the SO(d) symmetric vacua with all possible values of d within the range $2 \le d \le 7$, and observe clear indication of plateaus in the parameter space of the Gaussian action, which is crucial for the results to be reliable. The obtained results indeed exhibit systematic dependence on d, which turns out to be surprisingly similar to what was observed recently in an analogous work on the six-dimensional version of the model. In particular, we find the following properties: i) the extent in the shrunken directions is given by a constant, which does not depend on d; ii) the ten-dimensional volume of the Euclidean space-time is given by a constant, which does not depend on d except for d = 2; iii) The free energy takes the minimum value at d = 3. Intuitive understanding of these results is given by using the low-energy effective theory and some Monte Carlo results.

hep-th↗

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

A practical solution to the sign problem in a matrix model for dynamical compactification

The matrix model formulation of superstring theory offers the possibility to understand the appearance of 4d space-time from 10d as a consequence of spontaneous breaking of the SO(10) symmetry. Monte Carlo studies of this issue is technically difficult due to the so-called sign problem. We present a practical solution to this problem generalizing the factorization method proposed originally by two of the authors (K.N.A. and J.N.). Explicit Monte Carlo calculations and large-N extrapolations are performed in a simpler matrix model with similar properties, and reproduce quantitative results obtained previously by the Gaussian expansion method. Our results also confirm that the spontaneous symmetry breaking indeed occurs due to the phase of the fermion determinant, which vanishes for collapsed configurations. We clarify various generic features of this approach, which would be useful in applying it to other statistical systems with the sign problem.

hep-lat↗

arXiv2011

A general approach to the sign problem - the factorization method with multiple observables

The sign problem is a notorious problem, which occurs in Monte Carlo simulations of a system with the partition function whose integrand is not real positive. The basic idea of the factorization method applied on such a system is to control some observables in order to determine and sample efficiently the region of configuration space which gives important contribution to the partition function. We argue that it is crucial to choose appropriately the set of the observables to be controlled in order for the method to work successfully in a general system. This is demonstrated by an explicit example, in which it turns out to be necessary to control more than one observables. Extrapolation to large system size is possible due to the nice scaling properties of the factorized functions, and known results obtained by an analytic method are shown to be consistently reproduced.

cond-mat.stat-mech↗

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↗

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.

hep-lat↗

arXiv2010

A Study of the Complex Action Problem in a Simple Model for Dynamical Compactification in Superstring Theory Using the Factorization Method

The IIB matrix model proposes a mechanism for dynamically generating four dimensional space--time in string theory by spontaneous breaking of the ten dimensional rotational symmetry $\textrm{SO}(10)$. Calculations using the Gaussian expansion method (GEM) lend support to this conjecture. We study a simple $\textrm{SO}(4)$ invariant matrix model using Monte Carlo simulations and we confirm that its rotational symmetry breaks down, showing that lower dimensional configurations dominate the path integral. The model has a strong complex action problem and the calculations were made possible by the use of the factorization method on the density of states $ρ_n(x)$ of properly normalized eigenvalues $\tildeλ_n$ of the space--time moment of inertia tensor. We study scaling properties of the factorized terms of $ρ_n(x)$ and we find them in agreement with simple scaling arguments. These can be used in the finite size scaling extrapolation and in the study of the region of configuration space obscured by the large fluctuations of the phase. The computed values of $\tildeλ_n$ are in reasonable agreement with GEM calculations and a numerical method for comparing the free energy of the corresponding ansatze is proposed and tested.

hep-lat↗

arXiv2010

Spontaneous breaking of the rotational symmetry in dimensionally reduced super Yang-Mills models

We investigate the spontaneous breaking of the SO(D) symmetry in matrix models, which can be obtained by the zero-volume limit of pure SU(N) super Yang-Mills theory in D = 6, 10 dimensions. The D = 10 case corresponds to the IIB matrix model, which was proposed as a non-perturbative formulation of type IIB superstring theory, and the spontaneous breaking corresponds to the dynamical compactification of space-time suggested in that model. First we study the D = 6 case by the Gaussian expansion method, which turns out to yield clearer results than the previous results for the D = 10 case for certain technical reasons. By comparing the free energy of the SO(d) symmetric vacua for d = 2, 3, 4, 5, we conclude that the breaking SO(6) \to SO(3) actually occurs. We find that the extent of space-time in the shrunken directions is almost independent of d. In units of this universal scale, the extended directions seem to have large but still finite extents depending on d. We show that these results for the extent of space-time can be explained quantitatively by an argument based on the low-energy effective theory. With these new insights, we reconsider the previous results for the IIB matrix model, and find that they are also consistent with our argument based on the low-energy effective theory. Thus we arrive at comprehensive understanding and some quantitative predictions concerning the nature of the spontaneous symmetry breaking taking place in these models. The space-time picture that emerges from the IIB matrix model and its implication on possible interpretations of the model are also discussed.

hep-th↗

arXiv2010

Non-lattice simulation of supersymmetric gauge theories as a probe to quantum black holes and strings

In the past decade we have witnessed remarkable developments in the gauge-gravity duality, which suggested a new approach to superstring theory and quantum space-time. In this context it is important to study supersymmetric large-N gauge theories in the strongly coupled regime. I will summarize the results and insights obtained so far by non-lattice simulations. A simple example of the gauge-gravity duality is the one between 1d U(N) gauge theory with 16 supercharges and the so-called black 0-brane solution in type IIA supergravity. In order for this duality to be valid, one has to take the 't Hooft large-N limit and to take the strong coupling limit on the gauge theory side. The gauge theory can be regularized by fixing the gauge completely thanks to one dimension, and by introducing a Fourier mode cutoff. One can then use the standard RHMC algorithm to simulate the system. The energy calculated as a function of the temperature was compared with the results obtained from the gravity side based on the black hole thermodynamics. This confirmed the gauge-gravity duality with high accuracy and provided the microscopic origin of the black hole thermodynamics. From the calculation of the Wilson loop, one obtains the Schwarzschild radius of the dual geometry. One can actually use the present 1d model with supersymmetric mass deformation to study \mathcal{N}=4 super Yang-Mills theory on R \times S^3 based on a novel large-N reduction, which generalizes the original idea of Eguchi and Kawai. It is remarkable that we can now simulate the 4d superconformal field theory, which appears in the most typical case of the gauge-gravity duality known as the AdS/CFT correspondence. In particular, no fine-tuning is required unlike previous proposals based on the lattice regularization.

hep-lat↗

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

Dominance of a single topological sector in gauge theory on non-commutative geometry

We demonstrate a striking effect of non-commutative (NC) geometry on topological properties of gauge theory by Monte Carlo simulations. We study 2d U(1) NC gauge theory for various boundary conditions using a new finite-matrix formulation proposed recently. We find that a single topological sector dictated by the boundary condition dominates in the continuum limit. This is in sharp contrast to the results in commutative space-time based on lattice gauge theory, where all topological sectors appear with certain weights in the continuum limit. We discuss possible implications of this effect in the context of string theory compactifications and in field theory contexts.

hep-th↗

arXiv2009

Testing a novel large-N reduction for N=4 super Yang-Mills theory on RxS^3

Recently a novel large-N reduction has been proposed as a maximally supersymmetric regularization of N=4 super Yang-Mills theory on RxS^3 in the planar limit. This proposal, if it works, will enable us to study the theory non-perturbatively on a computer, and hence to test the AdS/CFT correspondence analogously to the recent works on the D0-brane system. We provide a nontrivial check of this proposal by performing explicit calculations in the large-N reduced model, which is nothing but the so-called plane wave matrix model, around a particular stable vacuum corresponding to RxS^3. At finite temperature and at weak coupling, we reproduce precisely the deconfinement phase transition in the N=4 super Yang-Mills theory on RxS^3. This phase transition is considered to continue to the strongly coupled regime, where it corresponds to the Hawking-Page transition on the AdS side. We also perform calculations around other stable vacua, and reproduce the phase transition in super Yang-Mills theory on the corresponding curved space-times such as RxS^3/Z_q and RxS^2.

hep-th↗

arXiv2009

Finite-matrix formulation of gauge theories on a non-commutative torus with twisted boundary conditions

We present a novel finite-matrix formulation of gauge theories on a non-commutative torus. Unlike the previous formulation based on a map from a square matrix to a field on a discretized torus with periodic boundary conditions, our formulation is based on the algebraic characterization of the configuration space. This enables us to describe the twisted boundary conditions in terms of finite matrices and hence to realize the Morita equivalence at a fully regularized level. Matter fields in the fundamental representation turn out to be represented by rectangular matrices for twisted boundary conditions analogously to the matrix spherical harmonics on the fuzzy sphere with the monopole background. The corresponding Ginsparg-Wilson Dirac operator defines an index, which can be used to classify gauge field configurations into topological sectors. We also perform Monte Carlo calculations for the index as a consistency check. Our formulation is expected to be useful for applications of non-commutative geometry to various problems related to topological aspects of field theories and string theories.

hep-th↗

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↗

arXiv2008

Schwarzschild radius from Monte Carlo calculation of the Wilson loop in supersymmetric matrix quantum mechanics

In the string/gauge duality it is important to understand how the space-time geometry is encoded in gauge theory observables. We address this issue in the case of the D0-brane system at finite temperature T. Based on the duality, the temporal Wilson loop operator W in gauge theory is expected to contain the information of the Schwarzschild radius R_{Sch} of the dual black hole geometry as log = R_{Sch} / (2 pi alpha' T). This translates to the power-law behavior log = 1.89 (T/lambda^{1/3})^{-3/5}, where lambda is the 't Hooft coupling constant. We calculate the Wilson loop on the gauge theory side in the strongly coupled regime by performing Monte Carlo simulation of supersymmetric matrix quantum mechanics with 16 supercharges. The results reproduce the expected power-law behavior up to a constant shift, which is explainable as alpha' corrections on the gravity side.

hep-th↗

arXiv2008

Deconfinement phase transition in N=4 super Yang-Mills theory on RxS^3 from supersymmetric matrix quantum mechanics

We test the recent claim that supersymmetric matrix quantum mechanics with mass deformation preserving maximal supersymmetry can be used to study N=4 super Yang-Mills theory on RxS^3 in the planar limit. When the mass parameter is large, we can integrate out all the massive fluctuations around a particular classical solution, which corresponds to RxS^3. The resulting effective theory for the gauge field moduli at finite temperature is studied both analytically and numerically, and shown to reproduce the deconfinement phase transition in N=4 super Yang-Mills theory on RxS^3 at weak coupling. This transition was speculated to be a continuation of the conjectured phase transition at strong coupling, which corresponds to the Hawking-Page transition based on the gauge-gravity duality. By choosing a different classical solution of the same model, one can also reproduce results for gauge theories on other space-time such as RxS^3/Z_q and RxS^2. All these theories can be studied at strong coupling by the new simulation method, which was used successfully for supersymmetric matrix quantum mechanics without mass deformation.

hep-th↗