2001/06/30 by Glenn Barnich, G. Barnich, Marc Henneaux +3
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Commutative property #Commutative ring #Cosmology and Gravitation Theories #Gauge theory #Geometry #Homogeneous space #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Physics #Pure mathematics #Quantum mechanics #Rigidity (electromagnetism) #Theoretical physics #hep-th
paper · pdf · doi:10.1088/1126-6708/2001/10/004
published as JHEP 0110:004,2001 · 18 pages Latex file, Section 5 on triviality of deformation removed, 1 reference added, minor misprints corrected, additional references in section 1
arxiv created 2001/09/07 · openalex publication_date 2001/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.