Noncommutative Two-Dimensional Gauge Theories

TL;DR

This paper explores the complex dynamics of noncommutative two-dimensional gauge theories, revealing how noncommutativity influences the mass spectrum and vacuum polarization, with implications for understanding noncommutative field theories.

Contribution

It provides a detailed analysis of noncommutative 2D gauge theories, highlighting the effects of noncommutativity on the mass spectrum and vacuum polarization, and comparing with commutative models.

Findings

Mass spectrum of noncommutative U(1) with adjoint matter resembles large-N SU(N) theory.

Noncommutative 't Hooft model shows non-trivial three-loop vacuum polarization.

Mass spectrum differs from commutative theories due to non-trivial noncommutativity effects.

Abstract

We elaborate on the dynamics of noncommutative two-dimensional gauge field theories. We consider U(N) gauge theories with fermions in either the fundamental or the adjoint representation. Noncommutativity leads to a rather non-trivial dependence on theta (the noncommutativity parameter) and to a rich dynamics. In particular the mass spectrum of the noncommutative U(1) theory with adjoint matter is similar to that of ordinary (commutative) two-dimensional large-N SU(N) gauge theory with adjoint matter. The noncommutative version of the 't Hooft model receives a non-trivial contribution to the vacuum polarization starting from three-loops order. As a result the mass spectrum of the noncommutative theory is expected to be different from that of the commutative theory.