Nonequivalent Seiberg-Witten maps for noncommutative massive U(N) gauge theory

TL;DR

This paper investigates the Seiberg-Witten map in noncommutative massive U(N) gauge theories, revealing that only specific solutions allow for consistent unitary gauge fixing, highlighting subtleties in noncommutative gauge invariance.

Contribution

It demonstrates the existence of non-equivalent Seiberg-Witten maps that affect gauge fixing in noncommutative massive gauge theories.

Findings

Only a particular class of Seiberg-Witten solutions admits unitary gauge fixing.

Nontrivial aspects arise in extending gauging mechanisms to noncommutative spaces.

The structure of Seiberg-Witten maps influences gauge invariance and quantization procedures.

Abstract

Massive vector fields can be described in a gauge invariant way with the introduction of compensating fields. In the unitary gauge one recovers the original formulation. Although this gauging mechanism can be extended to noncommutative spaces in a straightforward way, non trivial aspects show up when we consider the Seiberg-Witten map. As we show here, only a particular class of its solutions leads to an action that admits the unitary gauge fixing.