Proposal of a topological M(atrix) theory

Keeping in mind the several models of M(atrix) theory we attempt to understand the possible structure of the topological M(atrix) theory “underlying” these approaches. In particular we are motivated by the issue of the nature of the structure of the vacuum of the topological M(atrix) theory and how this could be related to the vacuum of the electroweak theory. In doing so we are led to a simple topological matrix model. Moreover, it is intuitively expected from current understanding that the noncommutative nature of “spacetime” and background independence should lead to a topological model. The main purpose of this paper is to propose a simple topological matrix model which bears a relation to F and M theories. Suggestions of the origin of the chemical potential term appearing in the matrix models are given.