2001/02/28 by Branislav Jurčo, Branislav Jurco, Peter Schupp +1 · 5 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #hep-th
paper · pdf · doi:10.1016/s0550-3213(01)00191-2
published as Nucl.Phys. B604 (2001) 148-180 · 38 pages, 1 figure; v2: references added
arxiv created 2001/02/28 · openalex publication_date 2001/06/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The concept of covariant coordinates on noncommutative spaces leads directly to gauge theories with generalized noncommutative gauge fields of the type that arises in string theory with background B-fields. The theory is naturally expressed in terms of cochains in an appropriate cohomology; we discuss how it fits into the framework of projective modules. The equivalence of star products that arise from the background field with and without fluctuations and Kontsevich's formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and noncommutative gauge theory (Seiberg-Witten map.) As application we show the exact equality of the Dirac-Born-Infeld action with B-field in the commutative setting and its semi-noncommutative cousin in the intermediate picture. Using noncommutative extra dimensions the construction is extended to noncommutative nonabelian gauge theory for arbitrary gauge groups; an explicit map between abelian and nonabelian gauge fields is given. All constructions are also valid for non-constant B-field, Poisson structure and metric.