On higher rank coisotropic AA-branes

This article is devoted to a world sheet analysis of AA-type DD-branes in N=(2,2)N=(2,2) supersymmetric non-linear sigma models. In addition to the familiar Lagrangian submanifolds with flat connection we reproduce the rank one AA-branes of Kapustin and Orlov, which are supported on coisotropic submanifolds. The main focus is however on gauge fields of higher rank and on tachyon profiles on brane–antibrane pairs. This will lead to the notion of a complex of coisotropic AA-branes. A particular role is played by the noncommutative geometry on the brane world volume. It ensures that brane–antibrane pairs localize again on coisotropic submanifolds.