A Metric Representation of Belavin's Yang-Mills Pseudoparticle Solution and Its Relation to Some Isotropic Universe
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 Stationary Soliton Solutions to the Five-Dimensional Vacuum Einstein Equation
abstract: We obtain an infinite number of soliton solutions to the five-dimensional stationary Einstein equation with axial symmetry by using the inverse scattering method. We start with the five-dimensional Minkowski space as a seed metric to obtain these solutions. The solutions are characterized by two soliton numbers and a constant appearing in the normalization factor which is related to a coordinate condition. We show that the (2,0)-soliton solution is identical to the Myers-Perry solution with one angular momentum variable by imposing a condition on the relation between parameters. We also show that the (2,2)-soliton solution is different from the black ring solution discovered by Emparan and Reall, although one component of the two metrics can be identical.

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: 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: 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: Equilibrium Condition of Dilaton Black Holes with Electric Charge

title: Monte Carlo studies of the spontaneous rotational symmetry breaking in dimensionally reduced super Yang-Mills models
abstract: A bstractIt has long been speculated that the spontaneous symmetry breaking (SSB) of SO(D) occurs in matrix models obtained by dimensionally reducing super Yang-Mills theory in D = 6, 10 dimensions. In particular, the D = 10 case corresponds to the IIB matrix model, which was proposed as a nonperturbative formulation of superstring theory, and the SSB may correspond to the dynamical generation of four-dimensional space-time. Recently, it has been shown by using the Gaussian expansion method that the SSB indeed occurs for D = 6 and D = 10, and interesting nature of the SSB common to both cases has been suggested. Here we study the same issue from first principles by a Monte Carlo method in the D = 6 case. In spite of a severe complex-action problem, the factorization method enables us to obtain various quantities associated with the SSB, which turn out to be consistent with the previous results obtained by the Gaussian expansion method. This also demonstrates the usefulness of the factorization method as a general approach to systems with the complex-action problem or the sign problem.

title: A practical solution to the sign problem in a matrix model for dynamical compactification
abstract: The matrix model formulation of superstring theory offers the possibility to understand the appearance of 4d space-time from 10d as a consequence of spontaneous breaking of the SO(10) symmetry. Monte Carlo studies of this issue is technically difficult due to the so-called sign problem. We present a practical solution to this problem generalizing the factorization method proposed originally by two of the authors (K.N.A. and J.N.). Explicit Monte Carlo calculations and large-N extrapolations are performed in a simpler matrix model with similar properties, and reproduce quantitative results obtained previously by the Gaussian expansion method. Our results also confirm that the spontaneous symmetry breaking indeed occurs due to the phase of the fermion determinant, which vanishes for collapsed configurations. We clarify various generic features of this approach, which would be useful in applying it to other statistical systems with the sign problem.

title: Dynamical aspects of the fuzzy CP2 in the large N reduced model with a cubic term
abstract: ``Fuzzy CP2'', which is a four-dimensional fuzzy manifold analogous to the fuzzy 2-sphere (S2), appears as a classical solution in the dimensionally reduced 8d Yang-Mills model with a cubic term involving the structure constant of the SU(3) Lie algebra. Although the fuzzy S2, which is also a classical solution of the same model, has actually smaller free energy than the fuzzy CP2, Monte Carlo simulation shows that the fuzzy CP2 is stable even nonperturbatively due to the suppression of tunneling effects at large N as far as the coefficient of the cubic term (?) is sufficiently large. As ? is decreased, both the fuzzy CP2 and the fuzzy S2 collapse to a solid ball and the system is essentially described by the pure Yang-Mills model (? = 0). The corresponding transitions are of first order. The gauge group generated dynamically above the critical point turns out to be of rank one for both CP2 and S2 cases. Above the critical point, we also perform perturbative calculations for various quantities to all orders, taking advantage of the one-loop saturation of the effective action in the large-N limit. By extrapolating our Monte Carlo results to N = ?, we find excellent agreement with the all order results.

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.

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