On The Complete Seiberg-Witten Map For Theories With Topological Terms

TL;DR

This paper formulates and solves the Seiberg-Witten map problem using BRST cohomology, revealing ambiguities linked to cohomological classes and applying this to noncommutative Chern-Simons and Maxwell-Chern-Simons theories.

Contribution

It provides a complete cohomological characterization of the Seiberg-Witten map, including ambiguities, and demonstrates how to relate noncommutative and commutative topological gauge theories.

Findings

Identifies cohomological classes associated with SW map ambiguities.

Derives $ heta$-dependent terms in the commutative action from noncommutative theories.

Shows how to map noncommutative Maxwell-Chern-Simons to commutative form.

Abstract

The SW map problem is formulated and solved in the BRST cohomological approach. The well known ambiguities of the SW map are shown to be associated to distinct cohomological classes. This analysis is applied to the noncommutative Chern-Simons action resulting in the emergence of $\theta$-dependent terms in the commutative action which come from the nontrivial ambiguities. It is also shown how a specific cohomological class can be choosen in order to map the noncommutative Maxwell-Chern-Simons theory into the commutative one.