SPACE–TIME AND MATTER IN THE IIB MATRIX MODEL — GAUGE SYMMETRY AND DIFFEOMORPHISM

Abstract

We pursue a study of the type-IIB matrix model as a constructive definition of a superstring. In this paper, we justify the interpretation of space–time as being a distribution of eigenvalues of matrices by showing that some low-energy excitations indeed propagate in it. In particular, we show that if the distribution consists of small clusters of size n, low-energy theory acquires local SU(n) gauge symmetry, and a plaquette action for the associated gauge boson is induced. We finally argue a possible identification of the diffeomorphism symmetry with a permutation group acting on the set of eigenvalues, and show that general covariance is realized in the low-energy effective theory, even though we do not have a manifest general covariance in the IIB matrix model action.