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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 BPSsaturated 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. *

We study large N behavior of the IIB matrix model using the equivalence between the IIB matrix model for finite N and a field theory on a non-commutative periodic lattice with N x N sites. We find that the large N dependences of correlation functions can be obtained by naively counting the number of fields in the field theory on the non-commutative periodic lattice. Furthermore the large N scaling behavior of the coupling constant g is determined if we impose that the expectation values of Wilson loops are calculable.Comment: 10 pages, LaTeX, To be appeared in Prog. Theor. Phys. 105, (2001

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) × (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 × N matrices in the fundamental representation.

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