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

• Published in: arXiv.org
• Main Authors: Barnich, G, Grigoriev, M, Henneaux, M
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 07.09.2001
• Subjects: Deformation
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.0106188

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.