An Infinite Number of Static Soliton Solutions to the 5D Einstein-Maxwell Equations with a Dilaton Field
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: Equilibrium Condition of Dilaton Black Holes with Electric Charge

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: 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: 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: 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

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: 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: Curved-space classical solutions of a massive supermatrix model
abstract: We investigate here a supermatrix model with a mass term and a cubic interaction. It is based on the super Lie algebra osp(1|32,R), which could play a role in the construction of the eleven-dimensional M-theory. This model contains a massive version of the IIB matrix model, where some fields have a tachyonic mass term. Therefore, the trivial vacuum of this theory is unstable. However, this model possesses several classical solutions where these fields build noncommutative curved spaces and these solutions are shown to be energetically more favorable than the trivial vacuum. In particular, we describe in details two cases, the SO(3)×SO(3)×SO(3) (three fuzzy 2-spheres) and the SO(9) (fuzzy 8-sphere) classical backgrounds.

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: Perturbative dynamics of fuzzy spheres at large N
abstract: We clarify some peculiar aspects of the perturbative expansion around a classical fuzzy-sphere solution in matrix models with a cubic term. While the effective action in the large-N limit is saturated at the one-loop level, we find that the ``one-loop dominance'' does not hold for generic observables due to one-particle reducible diagrams. However, we may exploit the one-loop dominance for the effective action and obtain various observables to all orders from one-loop calculation by simply shifting the center of expansion to the ``quantum solution'', which extremizes the effective action. We confirm the validity of this method by comparison with the direct two-loop calculation and with Monte Carlo results in the 3d Yang-Mills-Chern-Simons matrix model. From the all order result we find that the perturbative expansion has a finite radius of convergence.