Local BRST cohomology and Seiberg-Witten maps in noncommutative Yang-Mills theory

TL;DR

This paper explores the recursive construction and ambiguities of the Seiberg-Witten map in noncommutative Yang-Mills theory, analyzing local BRST cohomology and the impact of noncommutativity on conformal symmetries.

Contribution

It provides a detailed analysis of the Seiberg-Witten map construction and clarifies the structure of local BRST cohomology in noncommutative Yang-Mills theory.

Findings

Identified ambiguities in the Seiberg-Witten map construction.

Showed how noncommutative deformation obstructs some conformal symmetries.

Provided an exhaustive description of local BRST cohomology in this context.

Abstract

We analyze in detail the recursive construction of the Seiberg-Witten map and give an exhaustive description of its ambiguities. The local BRST cohomology for noncommutative Yang-Mills theory is investigated in the framework of the effective commutative Yang-Mills type theory. In particular, we show how some of the conformal symmetries get obstructed by the noncommutative deformation.