An N=2 worldsheet approach to D-branes in bihermitian geometries: I. Chiral and twisted chiral fields

TL;DR

This paper explores N=(2,2) supersymmetric sigma-models with boundaries, identifying D-brane configurations, constructing dualities between chiral and twisted chiral fields, and illustrating these with explicit examples like the WZW-model on S3xS1.

Contribution

It introduces explicit duality transformations between chiral and twisted chiral fields in bihermitian geometries while preserving supersymmetry, and studies D-branes in these contexts.

Findings

Identified D-brane configurations preserving N=2 supersymmetry.

Constructed duality transformations between chiral and twisted chiral fields.

Provided explicit examples including the WZW-model on S3xS1.

Abstract

We investigate N=(2,2) supersymmetric nonlinear sigma-models in the presence of a boundary. We restrict our attention to the case where the bulk geometry is described by chiral and twisted chiral superfields corresponding to a bihermitian bulk geometry with two commuting complex structures. The D-brane configurations preserving an N=2 worldsheet supersymmetry are identified. Duality transformations interchanging chiral for twisted chiral fields and vice versa while preserving all supersymmetries are explicitly constructed. We illustrate our results with various explicit examples such as the WZW-model on the Hopf surface S3xS1. The duality transformations provide e.g new examples of coisotropic A-branes on Kahler manifolds (which are not necessarily hyper-Kahler). Finally, by dualizing a chiral and a twisted chiral field to a semi-chiral multiplet, we initiate the study of D-branes in bihermitian geometries where the cokernel of the commutator of the complex structures is non-empty.