Seiberg-Witten maps from the point of view of consistent deformations of gauge theories

TL;DR

This paper explores the theoretical foundation of Seiberg-Witten maps as consistent deformations of gauge theories, linking their existence to cohomological theorems and illustrating with a noncommutative Freedman-Townsend model.

Contribution

It provides a cohomological perspective on the existence of Seiberg-Witten maps and interprets them as canonical transformations in the antifield formalism.

Findings

Seiberg-Witten maps relate commutative and noncommutative gauge theories via cohomological conditions.

The maps are characterized as canonical transformations in the antibracket formalism.

Application to noncommutative Freedman-Townsend theory demonstrates the approach.

Abstract

Noncommutative versions of theories with a gauge freedom define (when they exist) consistent deformations of their commutative counterparts. General aspects of Seiberg-Witten maps are discussed from this point of view. In particular, the existence of the Seiberg-Witten maps for various noncommutative theories is related to known cohomological theorems on the rigidity of the gauge symmetries of the commutative versions. In technical terms, the Seiberg-Witten maps define canonical transformations in the antibracket that make the solutions of the master equation for the commutative and noncommutative versions coincide in their antifield-dependent terms. As an illustration, the on-shell reducible noncommutative Freedman-Townsend theory is considered.