On the spectrum of particles created in a Robertson-Walker universe
Created particle spectra are calculated in Robertson-Walker universes with scale factora∝tα(0 <α≦ 1) anda∝et, and discussed with a special emphasis on their dependence upon the initial and final times at which a WKB-like positive frequency condition should be imposed. It is shown that the obtained spectra are very sensitive to these times if the WKB approximation for the field equation is not valid in their neighborhood. It is also shown that the total number density of created particles remains finite if the final time is set to be finite.

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: De Sitter metric as a self-consistent solution of the back reaction problem
abstract: The de Sitter metric is a solution of the Einstein equation even when quantum effects of matter fields are included. However between the curvature and the cosmological constant Λ changes drastically. For some values of Λ, there are two or three solutions, while there is none in some other cases. There can be even a positive curvature solution for negative Λ. These features depend on mass and spin of matter fields and the matter-curvature coupling.

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: Equilibrium Condition of Dilaton Black Holes with Electric Charge

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: Impact of supersymmetry on the nonperturbative dynamics of fuzzy spheres
abstract: We study a 4d supersymmetric matrix model with a cubic term, which incorporates fuzzy spheres as classical solutions, using Monte Carlo simulations and perturbative calculations. The fuzzy sphere in the supersymmetric model turns out to be always stable if the large-N limit is taken in such a way that various correlation functions scale. This is in striking contrast to analogous bosonic models, where the fuzzy sphere decays into the pure Yang-Mills vacuum due to quantum effects when the coefficient of the cubic term becomes smaller than a critical value. We also find that the power-law tail of the eigenvalue distribution, which exists in the supersymmetric model without the cubic term, disappears in the presence of the fuzzy sphere in the large-N limit. Coincident fuzzy spheres turn out to be unstable, which implies that the dynamically generated gauge group is U(1).

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: 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: Supermatrix Models
abstract: We investigate several matrix models based on super Lie algebras, osp(1|32, R), u(1|16, 16) and gl(1|32, R). They are natural generalizations of IIB matrix model and were first proposed by Smolin . In particular, we study the supersymmetry structures of these models and discuss possible reductions to IIB matrix model. We also point out that diffeomorphism invariance is hidden in gauge theories on noncommutative space which are derived from matrix models. This symmetry is independent of the global SO(9, 1) invariance in IIB matrix model and we report our trial to extend the global Lorentz invariance to local symmetry by introducing u(1|16, 16) or gl(1|32, R) super Lie algebras. ∗ e-mail address : azuma@gauge.scphys.kyoto-u.ac.jp † e-mail address : satoshi.iso@kek.jp ‡ e-mail address : hkawai@gauge.scphys.kyoto-u.ac.jp § e-mail address : yuhi@gauge.scphys.kyoto-u.ac.jp

title: General approach to the sign problem: Factorization method with multiple observables
abstract: 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 observable. 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.