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

Abstract

Non-commutative 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 non-commutative 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 non-commutative versions coincide in their an-tifield-dependent terms. As an illustration, the on-shell reducible non-commutative Freedman-Townsend theory is considered.