Topological Symmetry, Background Independence, and Matrix Models

TL;DR

This paper explores how topological symmetry breakdown relates to space-time uncertainty in matrix models, introduces new background-independent topological matrix models with p-brane solutions, and discusses unresolved fundamental issues.

Contribution

It presents a novel class of background-independent topological matrix models with p-brane solutions, linking topological symmetry breakdown to space-time uncertainty.

Findings

Space-time uncertainty principle linked to topological symmetry breakdown.

Construction of background-independent topological matrix models.

Existence of nontrivial p-brane solutions and classical space-time in these models.

Abstract

We illustrate a physical situation in which topological symmetry, its breakdown, space-time uncertainty principle, and background independence may play an important role in constructing and understanding matrix models. First, we show that the space-time uncertainty principle of string may be understood as a manifestation of the breakdown of the topological symmetry in the large $N$ matrix model. Next, we construct a new type of matrix models which is a matrix model analog of the topological Chern-Simons and BF theories. It is of interest that these topological matrix models are not only completely independent of the background metric but also have nontrivial "p-brane" solutions as well as commuting classical space-time as the classical solutions. In this paper, we would like to point out some elementary and unsolved problems associated to the matrix models, whose resolution would lead to the more satisfying matrix model in future.