The Renormalized Energy-Momentum Tensor In a Robertson -Walker Universe
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: Propagators for a Quantized Scalar Field in Some Isotropic Universe
abstract: To make clearer the relation examined in a previous paper between Chitre and Hartle's path-integral quantization procedure and our canonical one for a massive scalar field in a special isotropic universe, various propagators such as the 4-dimensional commutation func­ tion, the elementary solution and the associated Feynman propagator are explicitly deter­ mined. Owing to the determination, there arises a new changing procedure superior to the previous one from the isotropic expanding universe to the Minkowski space-time. Thus it is shown without any ambiguity that both the path-integral quantization procedure and our canonical one leading to the same pair-creation o£ particles as Chitre and Hartle's cannot recover the usual theory for a free field in the limit when the cosmic expansion disappears. (Notice, however, that our quantization procedure permits another case which can recover the Minkowski theory for a free field in the above limit, while it gives rise to no pair-creation.) Propagators for a massless scalar field are also dealt with in connection with the problem of conformal anomaly arising in the vacuum expectation value of the stress-energy tensor for our quantized scalar field, which is common to any quantized field in a curved space-time.

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.

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: 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: Perturbative versus nonperturbative dynamics of the fuzzy S2 × S2
abstract: 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: 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: 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: 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: 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.