Nonperturbative Dynamics of Noncommutative Gauge Theory

TL;DR

This paper develops a nonperturbative lattice framework for noncommutative gauge theories, establishing their equivalence with commutative theories and exploring their properties with matter fields.

Contribution

It introduces a lattice formulation for noncommutative Yang-Mills theories in arbitrary even dimensions and demonstrates Morita equivalence with commutative gauge theories.

Findings

Lattice regularization imposes finite volume, providing UV and IR cutoffs.

Morita equivalence between noncommutative and commutative gauge theories is explicitly shown.

Constructs observables in noncommutative gauge theories with matter fields.

Abstract

We present a nonperturbative lattice formulation of noncommutative Yang-Mills theories in arbitrary even dimension. We show that lattice regularization of a noncommutative field theory requires finite lattice volume which automatically provides both an ultraviolet and an infrared cutoff. We demonstrate explicitly Morita equivalence of commutative U(p) gauge theory with (p*n_f) flavours of fundamental matter fields on a lattice of size L with twisted boundary conditions and noncommutative U(1) gauge theory with n_f species of matter on a lattice of size (p*L) with single-valued fields. We discuss the relation with twisted large N reduced models and construct observables in noncommutative gauge theory with matter.