Monte Carlo studies of the GWW phase transition in large-N gauge theories
In the study of the small ten-dimensional Schwarzschild black hole, the black hole to string transition is an important problem. In [L. Alvarez-Gaume, P. Basu, M. Marino, S.R. Wadia,  (2006) 647 ], a possible identification is made between the Gross–Witten–Wadia (GWW) type third-order large- N phase transition in the boundary gauge theory and the string-black hole transition in the bulk. In this Letter, we exhibit the existence of the GWW transition by Monte Carlo simulation in the zero mode bosonic action of the finite-temperature N = 4 SYM theory on S 3 . Exhibiting this transition in the truncated but highly non-trivial gauge theory implies that in the vicinity of the critical temperature T c , the system goes critical, and the fluctuations give rise to universal formulas derived in [L. Alvarez-Gaume, P. Basu, M. Marino, S.R. Wadia,  (2006) 647, ]. We also discuss the issue of SO ( 6 ) R -symmetry breaking.

title: Matrix model with manifest general coordinate invariance
abstract: We present a formulation of a matrix model which manifestly possesses the general coordinate invariance when we identify the large N matrices with differential operators. In order to build a matrix model which has the local Lorentz invariance, we investigate how the so (9,1) Lorentz symmetry and the u ( N ) gauge symmetry are mixed together. We first analyze the bosonic part of the model, and we find that the Einstein gravity is reproduced in the classical low-energy limit. We then present a proposal to build a matrix model which has N =2 SUSY and reduces to the type IIB supergravity in the classical low-energy limit.

title: New states of gauge theories on a circle
abstract: A bstractWe study a one-dimensional large-N U(N) gauge theory on a circle as a toy model of higher dimensional Yang-Mills theories at finite temperature. To investigate the profile of the thermodynamical potential in this model, we evaluate a stochastic time evolution of several states, and find that an unstable confinement phase at high temperature does not decay to a stable deconfinement phase directly. Before it reaches the deconfinement phase, it develops to several intermediate states. These states are characterised by the expectation values of the Polyakov loop operators, which wind the temporal circle different times. We reveal that these intermediate states are the saddle point solutions of the theory, and similar solutions exist in a wide class of SU(N) and U(N) gauge theories on S1 including QCD and pure Yang-Mills theories in various dimensions. We also consider a Kaluza-Klein gravity, which is the gravity dual of the one-dimensional gauge theory on a spatial S1, and show that these solutions may be related to multi black holes localised on the S1. Then we present a connection between the stochastic time evolution of the gauge theory and the dynamical decay process of a black string though the Gregory-Laflamme instability.

title: Monte Carlo simulations of a supersymmetric matrix model of dynamical compactification in non perturbative string theory
abstract: The IKKT or IIB matrix model has been postulated to be a non perturbative definition of superstring theory. It has the attractive feature that spacetime is dynamically generated, which makes possible the scenario of dynamical compactification of extra dimensions, which in the Euclidean model manifests by spontaneously breaking the SO(10) rotational invariance (SSB). In this work we study using Monte Carlo simulations the 6 dimensional version of the Euclidean IIB matrix model. Simulations are found to be plagued by a strong complex action problem and the factorization method is used for effective sampling and computing expectation values of the extent of spacetime in various dimensions. Our results are consistent with calculations using the Gaussian Expansion method which predict SSB to SO(3) symmetric vacua, a finite universal extent of the compactified dimensions and finite spacetime volume.

title: The instability of intersecting fuzzy spheres
abstract: We discuss the classical and quantum stability of general configurations representing many fuzzy spheres in dimensionally reduced Yang-Mills-Chern-Simons models with and without supersymmetry. By performing one-loop perturbative calculations around such configurations, we find that intersecting fuzzy spheres are classically unstable in the class of models studied in this paper. We also discuss the large-N limit of the one-loop effective action as a function of the distance of fuzzy spheres. This shows, in particular, that concentric fuzzy spheres with different radii, which are identified with the 't Hooft-Polyakov monopoles, are perturbatively stable in the bosonic model and in the D = 10 supersymmetric model.

title: Dynamical generation of gauge groups in the massive Yang-Mills-Chern-Simons matrix model
abstract: It has been known that the dynamics of $k$ coincident D-branes in string theory is described effectively by $\mathrm{U}(k)$ 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 $k\ensuremath{\ne}1$ case as the true vacuum. The massive Yang-Mills\char21{}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 $\mathrm{O}(N)$ 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 Berenstein-Maldacena-Nastase (BMN) matrix model as coinciding transverse 5-branes in M-theory.

title: Propagators for a Quantized Scalar Field in a Static Closed Universe

title: An Infinite Number of Static Soliton Solutions to the 5D Einstein-Maxwell Equations
abstract: The soliton technique is applied to the 5D static Einstein-Maxwell equations, and an infinite number of solutions are explicitly obtained. We study the rod structure of 2-soliton solutions and we show that the 5D Reissner-Nordstrom solution and the 5D Majumdar-Papapetrou solution are included as the 2-soliton solutions.

title: Multi-Weyl Solutions to the Einstein Equation Coupled with Scalar Field
abstract: We study the static Einstein equation coupled with a scalar field with axial symmetry. The zero curvature equation both for the scalar field and a part of the metric in the scalar-Einstein equation enables one to obtain soliton solutions for both the scalar field and the metric. Of the infinite series of solutions for the metric and the scalar field we focus on the solution composed of 4-soliton solution of metric and 4-soliton solution of scalar field. We give a physical interpretation of the solution that two Weyls with scalar charges are exactly sustained by the tension of a string lying between the two Weyls. One of the most interesting problems of black holes is the study of bifurcation of a black hole and coalescence of multi black holes_ Before the dynamical behaviors of black holes is understood through the exact solutions of the Einstein equation, we should first understand the static and stationary solutions of multi black holes. In the preceding papers!) we have studied the vacuum soliton solutions to the static Einstein equation which includes the ring-type solutions and the multi-Weyl solution. In the 4-soliton solution or two-Weyl solution, what is peculiar in the solution is the exis­ tence of a conical singularity which may be interpreted as a "cosmic string" or strut between two Weyls. We showed that the string tension cancels the gravitational attractive force. There are two possible solutions which satisfy the asymptotic flatness: (i) The masses of two Weyls could be both positive while the string tension or the line density of the strut is negative; (ii) One of the masses of two Weyls should be negative if the string tension has the positive sign_ Either case comprises physical difficulty: negative mass or negative energy density. Classically there can be several ways for particles to balance despite of their attractive gravitational forces. The first is the introduction of strut to sustain their gravitational forces. The second is the introduction of negative mass to the system of particles. The third is the introduction of another force which can cancel the gravitational attractive force. As for the third one of the realization in the general relativity is the work by Papapetrou and Majumdar (the PM solution)_2) They introduced the coulomb force to cancel the gravitational attractive force. However the electric charge and the mass of each black hole are not independent charges but should satisfy the relation which realizes the extremal case of the Reissner-Nordstrom solution. What if the constraint between the mass and the electric charge are removed? This has not been answered so far. In the general relativity what could be the correspondence to the strut and the negative mass for balancing? This can be answered by showing the exact solutions to the Einstein equation. As far as we consider the vacuum Einstein equation we could not find physically

title: An Infinite Number of Static Soliton Solutions to the 5D Einstein-Maxwell Equations with a Dilaton Field
abstract: We study the 5D static Einstein-Maxwell equations with a dilaton field. We develop an infinite number of solutions using a soliton technique. We study the rod structure of a two-soliton solution and show that a 5D dilatonic black ring and black hole solutions are included.

title: The Singularity Structure of a Soliton Solution to the Higher-Dimensional Einstein Equations
abstract: We study a stationary and axisymmetric solution to the higher-dimensional Einstein equations and investigate its singularity structure. The solution consists of two solitons in the four-dimensional part (i.e., the Kerr solution) and n solitons in the extra dimensions. Naked singularities appear on the symmetry axis (z-axis) and/or at the event horizons of the Kerr solution. In a certain choice of integration constants there are solutions with regular event horizons