Comments, Questions and Proposal of a Topological M(atrix) Theory

TL;DR

This paper explores the structure of topological M(atrix) theory, proposing a simple topological matrix model that relates to F and M theories, and discusses the vacuum structure and noncommutative spacetime aspects.

Contribution

It introduces a new simple topological matrix model related to M and F theories, addressing vacuum structure and noncommutative spacetime.

Findings

Proposes a simple topological matrix model linked to M and F theories.

Discusses the vacuum structure of topological M(atrix) theory.

Suggests origins for the chemical potential term in matrix models.

Abstract

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 raise the issue about 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 expected from the current understanding that the noncommutative nature of ``spacetime'' and background independence should lead to Topological Model. The main purpose of this note is to propose a simple Topological Matrix Model which bears relation to F and M theories. Suggestions on the origin of the chemical potential term appearing in the matrix models are given.