TL;DR
This paper explores higher rank coisotropic A-branes in supersymmetric sigma models, focusing on gauge fields, tachyon profiles, and noncommutative geometry, leading to the concept of a complex of coisotropic A-branes.
Contribution
It extends the understanding of A-branes by analyzing higher rank gauge fields and tachyon profiles, introducing the notion of a complex of coisotropic A-branes.
Findings
Higher rank gauge fields on coisotropic A-branes are analyzed.
Brane-antibrane pairs localize on coisotropic submanifolds due to noncommutative geometry.
The concept of a complex of coisotropic A-branes is introduced.
Abstract
This article is devoted to a world sheet analysis of A-type D-branes in N=(2,2) supersymmetric non-linear sigma models. In addition to the familiar Lagrangian submanifolds with flat connection we reproduce the rank one A-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 A-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.
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