Matrix universality of gauge and gravitational dynamics

TL;DR

This paper introduces a simple cubic matrix model that can reproduce various gauge and gravity theories, suggesting a universal framework that connects different fundamental interactions through transformations mixing symmetries.

Contribution

It proposes a matrix model framework capable of deriving multiple gauge and gravity theories, including general relativity and Yang-Mills, highlighting a potential universality class of fundamental theories.

Findings

Matrix model leads to Chern-Simons, BF, and Einstein gravity theories.

Quantum corrections can produce coupled Einstein-Yang-Mills theories.

Universality classes connect diverse gauge and gravity theories through symmetry transformations.

Abstract

A simple cubic matrix model is presented, which has truncations that, it is argued, lead at the classical level to a variety of theories of gauge fields and gravity. These include Chern-Simons theory in d=3, and BF theory and general relativity in d=4. General relativity coupled to Yang-mills theory for any SU(N) may also arise from quantum corrections. On the basis of these results we conjecture that there are large universality classes of cut-off gauge and gravity theories, connected by transformations that mix up local and spacetime symmetries. If our universe is described by one of these theories then the question of the choice of the laws of physics is to a large extent subsumed in the problem of the choice of initial conditions in cosmology.