Perturbative versus nonperturbative dynamics of the fuzzy S2 × S2
We study a matrix model with a cubic term, which incorporates both the fuzzy S2 × S2 and the fuzzy S2 as classical solutions. Both of the solutions decay into the vacuum of the pure Yang-Mills model (even in the large-N limit) when the coefficient of the cubic term is smaller than a critical value, but the large-N behavior of the critical point is different for the two solutions. The results above the critical point are nicely reproduced by the all order calculations in perturbation theory. By comparing the free energy, we find that the true vacuum is given either by the fuzzy S2 or by the ``pure Yang-Mills vacuum'' depending on the coupling constant. In Monte Carlo simulation we do observe a decay of the fuzzy S2 × S2 into the fuzzy S2 at moderate N, but the decay probability seems to be suppressed at large N. The above results, together with our previous results for the fuzzy CP2, reveal certain universality in the large-N dynamics of four-dimensional fuzzy manifolds realized in a matrix model with a cubic term.

title: Towards an Effective Importance Sampling in Monte Carlo Simulations of a System with a Complex Action
abstract: The sign problem is a notorious problem, which occurs in Monte Carlo simulations of a system with a partition function whose integrand is not positive. One way to simulate such a system is to use the factorization method where one enforces sampling in the part of the configuration space which gives important contribution to the partition function. This is accomplished by using constraints on some observables chosen appropriately and minimizing the free energy associated with their joint distribution functions. These observables are maximally correlated with the complex phase. Observables not in this set essentially decouple from the phase and can be calculated without the sign problem in the corresponding "microcanonical" ensemble. These ideas are applied on a simple matrix model with very strong sign problem and the results are found to be consistent with analytic calculations using the Gaussian Expansion Method.

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: 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: 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: 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: 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: 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: 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: Multi-Weyl Solutions to the Einstein Equation Coupled with Scalar Field
abstract: We study the static Einstein equation coupled with a scalar field with axial symmetry. The zero curvature equation both for the scalar field and a part of the metric in the scalar-Einstein equation enables one to obtain soliton solutions for both the scalar field and the metric. Of the infinite series of solutions for the metric and the scalar field we focus on the solution composed of 4-soliton solution of metric and 4-soliton solution of scalar field. We give a physical interpretation of the solution that two Weyls with scalar charges are exactly sustained by the tension of a string lying between the two Weyls. One of the most interesting problems of black holes is the study of bifurcation of a black hole and coalescence of multi black holes_ Before the dynamical behaviors of black holes is understood through the exact solutions of the Einstein equation, we should first understand the static and stationary solutions of multi black holes. In the preceding papers!) we have studied the vacuum soliton solutions to the static Einstein equation which includes the ring-type solutions and the multi-Weyl solution. In the 4-soliton solution or two-Weyl solution, what is peculiar in the solution is the exis­ tence of a conical singularity which may be interpreted as a "cosmic string" or strut between two Weyls. We showed that the string tension cancels the gravitational attractive force. There are two possible solutions which satisfy the asymptotic flatness: (i) The masses of two Weyls could be both positive while the string tension or the line density of the strut is negative; (ii) One of the masses of two Weyls should be negative if the string tension has the positive sign_ Either case comprises physical difficulty: negative mass or negative energy density. Classically there can be several ways for particles to balance despite of their attractive gravitational forces. The first is the introduction of strut to sustain their gravitational forces. The second is the introduction of negative mass to the system of particles. The third is the introduction of another force which can cancel the gravitational attractive force. As for the third one of the realization in the general relativity is the work by Papapetrou and Majumdar (the PM solution)_2) They introduced the coulomb force to cancel the gravitational attractive force. However the electric charge and the mass of each black hole are not independent charges but should satisfy the relation which realizes the extremal case of the Reissner-Nordstrom solution. What if the constraint between the mass and the electric charge are removed? This has not been answered so far. In the general relativity what could be the correspondence to the strut and the negative mass for balancing? This can be answered by showing the exact solutions to the Einstein equation. As far as we consider the vacuum Einstein equation we could not find physically

title: On the spectrum of particles created in a Robertson-Walker universe
abstract: 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.