Shinji Shimasaki

N = 4 super Yang-Mills theory from the plane wave matrix model

We propose a nonperturbative definition of N=4 super Yang-Mills (SYM). We realize N=4 SYM on RxS{sup 3} as the theory around a vacuum of the plane wave matrix model. Our regularization preserves 16 supersymmetries and the gauge symmetry. We perform the 1-loop calculation to give evidences that the superconformal symmetry is restored in the continuum limit.

Embedding of theories with SU(2|4) symmetry into the plane wave matrix model

We study theories with SU(2|4) symmetry, which include the plane wave matrix model, 2+1 SYM on R ? S2 and = 4 SYM on R ? S3/Zk. All these theories possess many vacua. From Lin-Maldacenas method which gives the gravity dual of each vacuum, it is predicted that the theory around each vacuum of 2+1 SYM on R ? S2 and = 4 SYM on R ? S3/Zk is embedded in the plane wave matrix model. We show this directly on the gauge theory side. We clearly reveal relationships among the spherical harmonics on S3, the monopole harmonics and the harmonics on fuzzy spheres. We extend the compactification (the T-duality) in matrix models a la Taylor to that on spheres.

Gauge-Higgs Unification and Quark-Lepton Phenomenology in the Warped Spacetime

In the dynamical gauge-Higgs unification of electroweak interactions in the Randall-Sundrum warped spacetime, the Higgs boson mass is predicted in the range 120-290 GeV, provided that the spacetime structure is determined at the Planck scale. Couplings of quarks and leptons to gauge bosons and their Kaluza-Klein excited states are determined by the masses of quarks and leptons. All quarks and leptons other than top quarks have very small couplings to the Kaluza-Klein excited states of gauge bosons. The universality of weak interactions is slightly broken by magnitudes of 10{sup -8}, 10{sup -6}, and 10{sup -2} for {mu}-e, {tau}-e and t-e, respectively. Yukawa couplings become substantially smaller than those in the standard model, by a factor cos(1/2){theta}{sub W} where {theta}{sub W} is the non-Abelian Aharonov-Bohm phase (the Wilson line phase) associated with dynamical electroweak symmetry breaking.

New Insights into the Problem with a Singular Drift Term in the Complex Langevin Method

The complex Langevin method aims at performing path integral with a complex action numerically based on complexification of the original real dynamical variables. One of the poorly understood issues concerns occasional failure in the presence of logarithmic singularities in the action, which appear, for instance, from the fermion determinant in finite density QCD. We point out that the failure should be attributed to the breakdown of the relation between the complex weight that satisfies the Fokker-Planck equation and the probability distribution associated with the stochastic process. In fact, this problem can occur in general when the stochastic process involves a singular drift term. We show, however, in a simple example that there exists a parameter region in which the method works although the standard reweighting method is hardly applicable.

LARGE N REDUCTION ON GROUP MANIFOLDS

We show that the large N reduction holds on group manifolds. Large N field theories defined on group manifolds are equivalent to some corresponding matrix models. For instance, gauge theories on S3 can be regularized in a gauge invariant and SO(4) invariant manner.

Argument for justification of the complex Langevin method and the condition for correct convergence

The complex Langevin method is a promising approach to the complex-action problem based on a fictitious time evolution of complexified dynamical variables under the influence of a Gaussian noise. Although it is known to have a restricted range of applicability, the use of gauge cooling made it applicable to various interesting cases including finite density QCD in certain parameter regions. In this paper, we revisit the argument for justification of the method. In particular, we point out a subtlety in the use of time-evolved observables, which play a crucial role in the previous argument. This requires that the probability of the drift term should fall off exponentially or faster at large magnitude. We argue that this is actually a necessary and sufficient condition for the method to be justified. Using two simple examples, we show that our condition tells us clearly whether the results obtained by the method are trustable or not. We also discuss a new possibility for the gauge cooling, which can reduce the magnitude of the drift term directly.

T-duality, fiber bundles and matrices

We extend the T-duality for gauge theory to that on curved space described as a nontrivial fiber bundle. We also present a new viewpoint concerning the consistent truncation and the T-duality for gauge theory and discuss the relation between the vacua on the total space and on the base space. As examples, we consider S3(/Zk), S5(/Zk) and the Heisenberg nilmanifold.

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

We perform a systematic, large-scale lattice simulation of D0-brane quantum mechanics. The large-

Gauge cooling for the singular-drift problem in the complex Langevin method — a test in Random Matrix Theory for finite density QCD

N

On Relationships among Chern-Simons Theory, BF Theory and Matrix Model

and continuum limits of the gauge theory are taken for the first time at various temperatures