arXiv subjects

Jun Nishimura

Publications and source records attributed to Jun Nishimura.

At least 145 records · Page 8Linked to original sources

arXiv2005

The Large N Reduction in Matrix Quantum Mechanics -- a Bridge between BFSS and IKKT --

The large N reduction is an equivalence between large N gauge theories and matrix models discovered by Eguchi and Kawai in the early 80s. In particular the continuum version of the quenched Eguchi-Kawai model may be useful in studying supersymmetric and/or chiral gauge theories nonperturbatively. We apply this idea to matrix quantum mechanics, which is relevant, for instance, to nonperturbative studies of the BFSS Matrix Theory, a conjectured nonperturbative definition of M-theory. In the bosonic case we present Monte Carlo results confirming the equivalence directly, and discuss a possible explanation based on the Schwinger-Dyson equations. In the supersymmetric case we argue that the equivalence holds as well although some care should be taken if the rotational symmetry is spontaneously broken. This equivalence provides an explicit relation between the BFSS model and the IKKT model, which may be used to translate results in one model to the other.

hep-th↗

arXiv2005

Dynamical generation of gauge groups in the massive Yang-Mills-Chern-Simons matrix model

It has been known for some time that the dynamics of k coincident D-branes in string theory is described effectively by U(k) Yang-Mills theory at low energy. While these configurations appear as classical solutions in matrix models, it was not clear whether it is possible to realize the k =/= 1 case as the true vacuum. The massive Yang-Mills-Chern-Simons matrix model has classical solutions corresponding to all the representations of the SU(2) algebra, and provides an opportunity to address the above issue on a firm ground. We investigate the phase structure of the model, and find in particular that there exists a parameter region where O(N) copies of the spin-1/2 representation appear as the true vacuum, thus realizing a nontrivial gauge group dynamically. Such configurations are analogous to the ones that are interpreted in the BMN matrix model as coinciding transverse 5-branes in M-theory.

hep-th↗

arXiv2004

Gaussian expansion analysis of a matrix model with the spontaneous breakdown of rotational symmetry

Recently the gaussian expansion method has been applied to investigate the dynamical generation of 4d space-time in the IIB matrix model, which is a conjectured nonperturbative definition of type IIB superstring theory in 10 dimensions. Evidence for such a phenomenon, which is associated with the spontaneous breaking of the SO(10) symmetry down to SO(4), has been obtained up to the 7-th order calculations. Here we apply the same method to a simplified model, which is expected to exhibit an analogous spontaneous symmetry breaking via the same mechanism as conjectured for the IIB matrix model. The results up to the 9-th order demonstrate a clear convergence, which allows us to unambiguously identify the actual symmetry breaking pattern by comparing the free energy of possible vacua and to calculate the extent of ``space-time'' in each direction.

hep-th↗

arXiv2004

Absence of a fuzzy $S^4$ phase in the dimensionally reduced 5d Yang-Mills-Chern-Simons model

We perform nonperturbative studies of the dimensionally reduced 5d Yang-Mills-Chern-Simons model, in which a four-dimensional fuzzy manifold, ``fuzzy S$^{4}$'', is known to exist as a classical solution. Although the action is unbounded from below, Monte Carlo simulations provide an evidence for a well-defined vacuum, which stabilizes at large $N$, when the coefficient of the Chern-Simons term is sufficiently small. The fuzzy S$^{4}$ prepared as an initial configuration decays rapidly into this vacuum in the process of thermalization. Thus we find that the model does not possess a ``fuzzy S$^{4}$ phase'' in contrast to our previous results on the fuzzy S$^{2}$.

hep-th↗

arXiv2004

Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term

Fuzzy spheres appear as classical solutions in a matrix model obtained via dimensional reduction of 3-dimensional Yang-Mills theory with the Chern-Simons term. Well-defined perturbative expansion around these solutions can be formulated even for finite matrix size, and in the case of $k$ coincident fuzzy spheres it gives rise to a regularized U($k$) gauge theory on a noncommutative geometry. Here we study the matrix model nonperturbatively by Monte Carlo simulation. The system undergoes a first order phase transition as we change the coefficient ($α$) of the Chern-Simons term. In the small $α$ phase, the large $N$ properties of the system are qualitatively the same as in the pure Yang-Mills model ($α=0$), whereas in the large $α$ phase a single fuzzy sphere emerges dynamically. Various `multi fuzzy spheres' are observed as meta-stable states, and we argue in particular that the $k$ coincident fuzzy spheres cannot be realized as the true vacuum in this model even in the large $N$ limit. We also perform one-loop calculations of various observables for arbitrary $k$ including $k=1$. Comparison with our Monte Carlo data suggests that higher order corrections are suppressed in the large $N$ limit.

hep-th↗

arXiv2004

On the relation between non-commutative field theories at theta = infinity and large N matrix field theories

It is well-known that non-commutative (NC) field theories at theta = infinity are ``equivalent'' to large N matrix field theories to all orders in perturbation theory, due to the dominance of planar diagrams. By formulating a NC field theory on the lattice non-perturbatively and mapping it onto a twisted reduced model, we point out that the above equivalence does not hold if the translational symmetry of the NC field theory is broken spontaneously. As an example we discuss NC scalar field theory, where such a spontaneous symmetry breakdown has been confirmed by Monte Carlo simulations.

hep-th↗

arXiv2004

Non-Commutativity of the Zero Chemical Potential Limit and the Thermodynamic Limit in Finite Density Systems

Monte Carlo simulations of finite density systems are often plagued by the complex action problem. We point out that there exists certain non-commutativity in the zero chemical potential limit and the thermodynamic limit when one tries to study such systems by reweighting techniques. This is demonstrated by explicit calculations in a Random Matrix Theory, which is thought to be a simple qualitative model for finite density QCD. The factorization method allows us to understand how the non-commutativity, which appears at the intermediate steps, cancels in the end results for physical observables.

hep-lat↗

arXiv2003

Testing the Gaussian expansion method in exactly solvable matrix models

The Gaussian expansion has been developed since early 80s as a powerful analytical method, which enables nonperturbative studies of various systems using `perturbative' calculations. Recently the method has been used to suggest that 4d space-time is generated dynamically in a matrix model formulation of superstring theory. Here we clarify the nature of the method by applying it to exactly solvable one-matrix models with various kinds of potential including the ones unbounded from below and of the double-well type. We also formulate a prescription to include a linear term in the Gaussian action in a way consistent with the loop expansion, and test it in some concrete examples. We discuss a case where we obtain two distinct plateaus in the parameter space of the Gaussian action, corresponding to different large-N solutions. This clarifies the situation encountered in the dynamical determination of the space-time dimensionality in the previous works.

hep-th↗

arXiv2003

Lattice Superstring and Noncommutative Geometry

Recent developments in superstring theory and noncommutative geometry are deeply related to the idea of Eguchi-Kawai reduction in large N gauge theories which dates back to early 80s. After a general review on this subject including revived interests in solving planar QCD, we present some results in the superstring matrix model suggesting the dynamical generation of 4d space-time due to the collapse of the eigenvalue distribution. We then discuss interesting dynamical properties of field theories in noncommutative geometry, which have been revealed by Monte Carlo simulations of twisted reduced models. We conclude with a comment on the recent proposal for a lattice construction of supersymmetric gauge theories based on reduced models.

hep-lat↗

arXiv2003

A New Method for Simulating QCD at Finite Density

We propose a new method for simulating QCD at finite density, where interesting phases such as the color superconductivity phase is conjectured to appear. The method is based on a general factorization property of distribution functions of observables, and it is therefore applicable to any system with a complex action. The so-called overlap problem is completely eliminated by the use of constrained simulations. We test this method in a Random Matrix Theory for finite density QCD, where we are able to reproduce the exact results for the quark number density. The achieved system size is large enough to extract the thermodynamic limit. Our results provide a clear understanding of how the expected first order phase transition is induced by the imaginary part of the action. We also discuss the noncommutativity of the zero chemical potential limit and the thermodynamic limit, which is relevant to recent Monte Carlo studies at small chemical potential.

hep-lat↗

arXiv2003

The Factorization Method for Simulating Systems With a Complex Action

We propose a method for Monte Carlo simulations of systems with a complex action. The method has the advantages of being in principle applicable to any such system and provides a solution to the overlap problem. We apply it in random matrix theory of finite density QCD where we compare with analytic results. In this model we find non--commutativity of the limits $μ\to 0$ and $N\to\infty$ which could be of relevance in QCD at finite density.

hep-lat↗

arXiv2003

Factorization Method for Simulating QCD at Finite Density

We propose a new method for simulating QCD at finite density. The method is based on a general factorization property of distribution functions of observables, and it is therefore applicable to any system with a complex action. The so-called overlap problem is completely eliminated by the use of constrained simulations. We test this method in a Random Matrix Theory for finite density QCD, where we are able to reproduce the exact results for the quark number density.

hep-lat↗

arXiv2003

Supersymetry on the Noncommutative Lattice

Built upon the proposal of Kaplan et.al. [hep-lat/0206109], we construct noncommutative lattice gauge theory with manifest supersymmetry. We show that such theory is naturally implementable via orbifold conditions generalizing those used by Kaplan {\sl et.al.} We present the prescription in detail and illustrate it for noncommutative gauge theories latticized partially in two dimensions. We point out a deformation freedom in the defining theory by a complex-parameter, reminiscent of discrete torsion in string theory. We show that, in the continuum limit, the supersymmetry is enhanced only at a particular value of the deformation parameter, determined solely by the size of the noncommutativity.

hep-lat↗

arXiv2002

Convergence of the Gaussian Expansion Method in Dimensionally Reduced Yang-Mills Integrals

We advocate a method to improve systematically the self-consistent harmonic approximation (or the Gaussian approximation), which has been employed extensively in condensed matter physics and statistical mechanics. We demonstrate the {\em convergence} of the method in a model obtained from dimensional reduction of SU($N$) Yang-Mills theory in $D$ dimensions. Explicit calculations have been carried out up to the 7th order in the large-N limit, and we do observe a clear convergence to Monte Carlo results. For $D \gtrsim 10$ the convergence is already achieved at the 3rd order, which suggests that the method is particularly useful for studying the IIB matrix model, a conjectured nonperturbative definition of type IIB superstring theory.

hep-th↗

arXiv2002

Dynamical Generation of Four-Dimensional Space-Time in the IIB Matrix Model

We study the spontaneous breakdown of SO(10) symmetry in the IIB matrix model, a conjectured nonperturbative definition of type IIB superstring theory in ten dimensions. Our analysis is based on a Gaussian expansion technique, which was originally proposed by Kabat-Lifschytz and applied successfully to the strong coupling dynamics of the Matrix Theory. We propose a prescription for including higher order corrections, which yields a rapid convergence in a simple example. This prescription is then applied to the IIB matrix model up to the third order. We find that the `self-consistency equations' allow various symmetry breaking solutions. Among them, the solution preserving SO(4) symmetry is found to have the smallest free energy. The value of the free energy comes closer to the analytic formula obtained by Krauth-Nicolai-Staudacher as we increase the order. The extent of the space-time in the 4 directions is larger than the remaining 6 directions, and the ratio increases with the order. These results provide the first analytical evidence that four-dimensional space-time is generated dynamically in the IIB matrix model.

hep-th↗

arXiv2001

Exactly Solvable Matrix Models for the Dynamical Generation of Space-Time in Superstring Theory

We present a class of solvable SO(D) symmetric matrix models with D bosonic matrices coupled to chiral fermions. The SO(D) symmetry is spontaneously broken due to the phase of the fermion integral. This demonstrates the conjectured mechanism for the dynamical generation of four-dimensional space-time in the IIB matrix model, which was proposed as a nonperturbative definition of type IIB superstring theory in ten dimensions.

hep-th↗

arXiv2000

Brane world from IIB matrices

We have recently proposed a dynamical mechanism that may realize a flat four-dimensional space time as a brane in type IIB superstring theory. A crucial role is played by the phase of the chiral fermion integral associated with the IKKT Matrix Theory, which is conjectured to be a nonperturbative definition of type IIB superstring theory. We demonstrate our mechanism by studying a simplified model, in which we find that a lower-dimensional brane indeed appears dynamically. We also comment on some implications of our mechanism on model building of the brane world.

hep-th↗

arXiv1999

Translational Anomaly in Chiral Gauge Theories on a Torus and the Overlap Formalism

We point out that a fermion determinant of a chiral gauge theory on a 2D torus has a phase ambiguity proportional to the Polyakov loops along the boundaries, which can be reproduced by the overlap formalism. We show that the requirement on the fermion determinant that a singularity in the gauge field can be absorbed by a change of the boundary condition for the fermions, is not compatible with translational invariance in general. As a consequence, the gauge anomaly for singular gauge transformations discovered by Narayanan-Neuberger actually exists in any 2D U(1) chiral gauge theory unless the theory is vector-like. We argue that the gauge anomaly is peculiar to the overlap formalism with the Wigner-Brillouin phase choice and that it is not necessarily a property required in the continuum. We also generalize our results to any even dimension.

hep-lat↗