N = 2 world-sheet approach to D-branes on generalized Kaehler geometries: I. General formalism

TL;DR

This paper develops a formalism using N=2 world-sheet superspace to describe D-branes on generalized Kaehler manifolds, providing a new classification approach that includes semi-chiral superfields.

Contribution

It introduces a general N=2 boundary superspace formalism for D-branes on bihermitian manifolds, including novel treatment of semi-chiral superfields.

Findings

Formalism for D-branes as boundary conditions in N=2 superspace

Classification scheme for D-branes on generalized Kaehler manifolds

Inclusion of semi-chiral superfields in the description

Abstract

We present an N = 2 world-sheet superspace description of D-branes on bihermitian or generalized Kaehler manifolds. To accomplish this, D-branes are considered as boundary conditions for a nonlinear sigma-model in what we call N = 2 boundary superspace. In this note the general formalism for such an approach is presented and the resulting classification sketched. This includes some remarks regarding target spaces whose parameterization includes semi-chiral superfields which have not appeared in the literature yet. In an accompanying note we turn to some examples and applications of the general setup presented here.