On noncommutative and commutative equivalence for BFYM theory : : Seiberg-Witten map

TL;DR

This paper constructs a Seiberg-Witten map for BFYM theory on commutative and noncommutative spaces, demonstrating their gauge equivalence and expressing the noncommutative action in terms of ordinary fields.

Contribution

It introduces a Seiberg-Witten map for BFYM theory, establishing gauge equivalence between commutative and noncommutative formulations and relating their actions.

Findings

Noncommutative BFYM action expressed in terms of ordinary fields.

Gauge equivalence established via Seiberg-Witten map.

Noncommutative and commutative theories shown to be related up to higher-dimensional terms.

Abstract

BFYM on commutative and noncommutative ${\mathbb{R}}^4$ is considered and a Seiberg-Witten gauge-equivalent transformation is constructed for these theories. Then we write the noncommutative action in terms of the ordinary fields and show that it is equivalent to the ordinary action up to higher dimensional gauge invariant terms.