BACKGROUND INDEPENDENT MATRIX MODELS

A class of background independent matrix models is made for which the structure of both local gauge symmetries and classical solutions is cl arified. These matrix models do not involve a space-time metric and pr ovide the matrix analogs of topological Chern-Simons and BF theories. It is explicitly shown that the BF type of matrix model can be formula ted in any space-time dimension and include 3 + 1 dimensional gravity as a special case. Moreover, we discuss some generalization of the mod el to include a fermionic BRST-like symmetry whose partition function is related to the Casson invariant. (C) 1998 Elsevier Science B.V. All rights reserved.