Large-N behaviors of the IIB matrix model and the regularized Schild models

We evaluate $N$ dependences of correlation functions in the bosonic part of the IIB matrix model by the Monte Carlo method. We also evaluate those in two sorts of regularized Schild models and find that the $N$ dependences are different from those in the matrix model. In particular, the distribution of the eigenvalues are logarithmically divergent in the regularized Schild model when $g^2N$ is fixed.Comment: 7 pages, 4 figures: minor changes, references added, to appear in JHE

Electro-magnetic Simulation Based on the Integral Form of Maxwell’s Equations

Algorithms for a computational method of electromagnetics based on the integral form of Maxwell’s equations are introduced. The algorithms are supported by the lowest- and next-to-the-lowest-order approximations of integrals over a cell surface and edge of the equations. The method supported by the lowest-order approximation of the integrals coincides with the original finite-difference time-domain (FDTD) method, a well-known computational method of electromagnetics based on the differential form of Maxwell’s equations. The method supported by the next-to-the-lowest-order approximation can be considered a correction to the FDTD method. Numerical results of an electromagnetic wave propagating in a two-dimensional slab waveguide using the original and the corrected FDTD methods are also shown to compare them with an analytical result. In addition, the results of the corrected FDTD method are also shown to be more accurate and reliable than those of the original FDTD method

Representation of SU(infinity) Algebra for Matrix Models

We investigate how the matrix representation of SU(N) algebra approaches that of the Poisson algebra in the large N limit. In the adjoint representation, the (N^2-1) times (N^2-1) matrices of the SU(N) generators go to those of the Poisson algebra in the large N limit. However, it is not the case for the N times N matrices in the fundamental representation.Comment: 8 page

Unitary IIB Matrix Model and the Dynamical Generation of the Space Time

We propose a unitary matrix model as a regularization of the IIB matrix model of Ishibashi-Kawai-Kitazawa-Tsuchiya (IKKT). The fermionic part is incorporated using the overlap formalism in order to avoid unwanted ``doublers'' while preserving the global gauge invariance. This regularization, unlike the one adopted by IKKT, has manifest U(1)^10 symmetry, which corresponds to the ten-dimensional translational invariance of the space time. We calculate one-loop effective action around some typical BPS-saturated configurations in the weak coupling limit. We also discuss a possible scenario for the dynamical generation of the four-dimensional space time through spontaneous breakdown of the U(1)^10 symmetry in the double scaling limit.Comment: 30 pages, 1 Postscript figure, The final version accepted by NP