New states of gauge theories on a circle
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: Investigation of Matrix Theory via Super Lie Algebra
abstract: This paper reports the investigation of a matrix model via super Lie algebra, following the proposal of L. Smolin. We consider the osp(1|32,R) nongauged matrix model and gl(1|32,R) gauged matrix model, especially paying attention to the supersymmetry and the relationship with IKKT model. This paper is based on the collaboration with the collaboration with S.Iso, H.Kawai and Y.Ohwashi.

title: Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term
abstract: 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.

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: A Study of the Complex Action Problem in a Simple Model for Dynamical Compactification in Superstring Theory Using the Factorization Method
abstract: 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 $\rho_n(x)$ of properly normalized eigenvalues $\tilde\lambda_n$ of the space--time moment of inertia tensor. We study scaling properties of the factorized terms of $\rho_n(x)$ 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 $\tilde\lambda_n$ are in reasonable agreement with GEM calculations and a numerical method for comparing the free energy of the corresponding ansatze is proposed and tested.

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: Classification of Spatially Flat Cosmological Solutions in the Presence of the Cosmological Constant and Backreaction of Conformally Invariant Quantum Fields
abstract: We find all the spatially flat Robertson-Walker type solutions of Einstein's equations with the cos· mological constant and quantum fluctuations of conformally invariant matter fields, which include effects of the conformal anomaly. We show that the relevant back-reaction equation is interpreted as an equation of motion for a classical one-dimensional potential problem with (anti·) dissipation. By consider­ ing the potential form, we can easily classify all the solutions and understand their qualitative behaviour, such as monotonic expansion (contraction), oscillation, contraction followed by expansion. Only two kinds of asymptotic behaviour are allowed, both in the past and in the future. They are (1) exponential expansion or contraction (asymptotically de Sitter) and (2) singularity (zero or infinity of the scale factor) at a finite cosmic time. Stability of de Sitter solutions (singular solutions) is also discussed. The Minkowski solution in the case of the vanishing cosmological constant is shown to be unstable, irrespectively of th~ sign of a parameter in the equation. .

title: Axially symmetric solution of the Einstein equation with solitons in extra dimensions
abstract: We give the solution to the higher dimensional Einstein equation with axial symmetry by using the inverse scattering method. The solution consists of two solitons in the external dimensions and any number of solitons in the internal dimensions.

title: The Renormalized Energy-Momentum Tensor In a Robertson -Walker Universe
abstract: An expectation value of the energy·momentum tensor for a massive scalar field propagating in a Robertson-\\;'alker universe is calculated by taking account of both effects caused by the particle creation and the vacuum polarization. A special case of the Chitre-Hartle universe which enables us to perform an explicit calculation is also treated.

title: A Metric Representation of Belavin's Yang-Mills Pseudoparticle Solution and Its Relation to Some Isotropic Universe
abstract: In order to investigate a physical connection between the quantum tunneling processes (vacuum-to vacuum transition or thermal radiation) of Yang-Mills 11 •*' and gravitational" pseudoparticles, T omimatsu"'<l compared several (especially, topological) properties of the Belavin and Schwarzschild solutions with each other in terms of their Euclidean metrics. For that purpose, he transformed the Belavin solution into a metric form on the basis of Carmeli's'l formalism which describes the general theory of relativity in the form of an SL (2, C) gauge field. He showed that, of the two important topological quantities P (the Pontryagin number) and X (the Euler characteristic), P= 0 and ;: '-2 for the rewritten Belavin solution, similar to the result that P= 0 and !: ~, 2 for the Schwarzschild solution. To assure the idea that the origin of radiation with a thermal nature from both pseudoparticles is due to the fact that their x's are non-vanishing, he"b' performed a path-integral approach to the quantization of a massive scalar field in the gravitational field corresponding to Belavin' s solution. The resulting energy spectrum was an incomplete thermal one because of its non -uniform temper a ture and non -zero

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.