Nonabelian noncommutative gauge fields and Seiberg-Witten map

Abstract

Noncommutative gauge fields (similar to the type that arises in string theory with background B-fields) are constructed for arbitrary nonabelian gauge groups with the help of a map that relates ordinary nonabelian and noncommutative gauge theories (Seiberg-Witten map). As in our previous work we employ Kontsevich's formality and the concept of equivalent star products. As a byproduct we obtain a ``Mini Seiberg-Witten map'' that explicitly relates ordinary abelian and nonabelian gauge fields.