Noncommutative Chern-Simons terms and the noncommutative vacuum

TL;DR

The paper explores how noncommutative parameters act as superselection parameters in gauge theories, leading to a generalized Chern-Simons action that influences vacuum structure and gauge theory behavior.

Contribution

It introduces a generic formula for noncommutative Chern-Simons terms that reduces to the standard form in the commutative limit and reveals new vacuum structures.

Findings

Noncommutative parameters act as superselection parameters.

A generalized Chern-Simons action includes lower-dimensional terms.

Vacuum structure is altered, enabling nonstandard gauge theories.

Abstract

It is pointed out that the space noncommutativity parameters $theta^{\mu \nu}$ in noncommutative gauge theory can be considered as a set of superselection parameters, in analogy with the theta-angle in ordinary gauge theories. As such, they do not need to enter explicitly into the action. A simple generic formula is then suggested to reproduce the Chern-Simons action in noncommutative gauge theory, which reduces to the standard action in the commutative limit but in general implies a cascade of lower-dimensional Chern-Simons terms. The presence of these terms in general alters the vacuum structure of the theory and nonstandard gauge theories can emerge around the new vacua.