Matrix Models of Noncommutative (2d+1) Lattice Gauge Theories

TL;DR

This paper explores how odd-dimensional noncommutative lattice gauge theories can be represented by matrix models using Morita equivalence, with explicit constructions for 3D NCQED and NCSQED.

Contribution

It provides explicit matrix model formulations for noncommutative 3D QED and scalar QED, advancing the understanding of their noncommutative gauge theories.

Findings

Explicit matrix models for 3D NCQED and NCSQED constructed.

Demonstrates the application of Morita equivalence in odd dimensions.

Facilitates nonperturbative studies of noncommutative gauge theories.

Abstract

We investigate the problem of mapping, through the Morita equivalence, odd dimensional noncommutative lattice gauge theories onto suitable matrix models. We specialize our analysis to noncommutative three dimensional QED (NCQED) and scalar QED (NCSQED), for which we explicitly build the corresponding Matrix Model.