Geometry of D-branes for general N=(2,2) sigma models

TL;DR

This paper describes D-branes in N=(2,2) sigma models using generalized Kahler geometry, showing their correspondence to (twisted) generalized complex submanifolds, including cases with non-trivial NS-flux.

Contribution

It provides a world-sheet description of D-branes via gluing conditions and links A- and B-type branes to (twisted) generalized complex submanifolds in a unified framework.

Findings

D-branes correspond to (twisted) generalized complex submanifolds.

A- and B-type branes are characterized by different (twisted) generalized complex structures.

The framework includes sigma models with non-trivial NS-flux.

Abstract

We give a world-sheet description of D-brane in terms of gluing conditions on T+T^*. Using the notion of generalized Kahler geometry we show that A- and B-types D-branes for the general N=(2,2) supersymmetric sigma model (including a non-trivial NS-flux) correspond to the (twisted) generalized complex submanifolds with respect to the different (twisted) generalized complex structures however.