The instability of intersecting fuzzy spheres
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: 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: 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: 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: 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: 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: Low-energy behavior of a quantized scalar field in the linearly expanding universe
abstract: We study positive frequency mode solutions of a massive scalar field at an initial stage in the spatially flat, linearly expanding Robertson-Walker universe. The essential point is that the initial time is taken to be small enough, but nonzero (e.g., the Planck time), and the mode is determined by a kind of WKB condition. We calculate the created particle spectrum, and show that its low-energy behavior is considerably different from the previous results.

title: On the Definition of a Positive Frequency Part for a Quantized Scalar Field in Several Robertson-Walker Universes

title: Classification of an infinite series of static solutions to the vacuum Einstein equations
abstract: We propose a classification of an infinite series of the static solutions to the vacuum Einstein equation by means of their soliton number and the real and/or complex pole trajectories. We also show that in the 4-soliton solution there appears an intriguing ring solution of which the curvature invariant has a finite limit at the rings.

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: 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.