An N=2 worldsheet approach to D-branes in bihermitian geometries: II. The general case

TL;DR

This paper completes the classification of supersymmetric D-branes in bihermitian geometries using N=(2,2) sigma-models, introducing new types of branes and dualities in generalized complex geometry.

Contribution

It extends the understanding of D-branes in bihermitian geometries by classifying all supersymmetric configurations and constructing duality transformations between superfield types.

Findings

Defined lagrangian and coisotropic branes in non-Kahler bihermitian manifolds.

Introduced hybrid branes interpolating between different types.

Constructed explicit duality transformations for superfields.

Abstract

We complete the investigation of N=(2,2) supersymmetric nonlinear sigma-models in the presence of a boundary. We study the full bihermitian geometry parameterized by chiral, twisted chiral and semi-chiral superfields and identify the D-brane configurations preserving an N=2 worldsheet supersymmetry. Combining twisted with semi-chiral superfields leads to a clearly defined notion of lagrangian and coisotropic branes generalizing lagrangian and coisotropic A-branes on Kahler manifolds to manifolds which are not necessarily Kahler (but still bihermitian). Adding chiral fields complicates the picture and results in hybrid configurations interpolating between lagrangian/coisotropic branes and branes wrapping around a holomorphic cycle. Even here the branes can be viewed as coisotropic submanifolds albeit in a generalized sense. All supersymmetric D-brane configurations are characterized in the context of generalized complex geometry. Duality transformations interchanging the various types of superfields while preserving all supersymmetries are explicitly constructed and provide for a powerful technique to construct various highly non-trivial D-brane configurations. Several explicit examples are given.