Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-02-20
Nucl.Phys. B604 (2001) 148-180
Physics
High Energy Physics
High Energy Physics - Theory
38 pages, 1 figure; v2: references added
Scientific paper
10.1016/S0550-3213(01)00191-2
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.
Jurco Branislav
Schupp Peter
Wess Julius
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