N=2 world-sheet approach to D-branes on generalized Kaehler geometries. Pt. 1. General formalism

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 σ-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. (Abstract Copyright [2009], Wiley Periodicals, Inc.)