Background Independent Matrix Models

TL;DR

This paper introduces background independent matrix models that generalize topological field theories, clarify their gauge symmetries and solutions, and connect to 3+1 dimensional gravity and topological invariants.

Contribution

It presents a new class of background independent matrix models that encompass topological theories and include gravity as a special case, with potential links to topological invariants.

Findings

Matrix models without a space-time metric are constructed.

BF type matrix models can be formulated in any dimension.

The model includes 3+1 dimensional gravity as a special case.

Abstract

A class of background independent matrix models is made for which the structure of both local gauge symmetries and classical solutions is clarified. These matrix models do not involve a space-time metric and provide the matrix analogs of topological Chern-Simons and BF theories. It is explicitly shown that the BF type of matrix model can be formulated in any space-time dimension and include 3+1 dimensional gravity as a special case. Moreover, we discuss some generalization of the model to include a fermionic BRST-like symmetry whose partition function is related to the Casson invariant.