Finite N Matrix Models of Noncommutative Gauge Theory

TL;DR

This paper introduces a unitary matrix model that discretizes noncommutative gauge theories, providing a lattice formulation that preserves star-gauge invariance and connects to non-perturbative definitions of noncommutative Yang-Mills theory.

Contribution

It constructs a novel lattice matrix model based on discrete projective modules over the noncommutative torus, enabling nonperturbative study of noncommutative gauge theories.

Findings

Model reduces to Wilson lattice gauge theory in special cases

Maintains finite spacetime volume and noncommutativity scale in continuum limit

Provides a framework for studying noncommutative gauge properties

Abstract

We describe a unitary matrix model which is constructed from discrete analogs of the usual projective modules over the noncommutative torus and use it to construct a lattice version of noncommutative gauge theory. The model is a discretization of the noncommutative gauge theories that arise from toroidal compactification of Matrix theory and it includes a recent proposal for a non-perturbative definition of noncommutative Yang-Mills theory in terms of twisted reduced models. The model is interpreted as a manifestly star-gauge invariant lattice formulation of noncommutative gauge theory, which reduces to ordinary Wilson lattice gauge theory for particular choices of parameters. It possesses a continuum limit which maintains both finite spacetime volume and finite noncommutativity scale. We show how the matrix model may be used for studying the properties of noncommutative gauge theory.