N=2 boundary conditions for non-linear sigma models and Landau-Ginzburg models -: art. no. 006

We study N = 2 nonlinear two dimensional sigma models with boundaries and their massive generalizations (the Landau-Ginzburg models). These models are defined over either Kahler or bihermitean target space manifolds. We determine the most general local N = 2 superconformal boundary conditions (D-branes) for these sigma models. In the Kahler case were produce the known results in a systematic fashion including interesting results concerning the coisotropic A-type branes. We further analyse the N = 2 superconformal boundary conditions for sigma models defined over a bihermitean manifold with torsion. We interpret the boundary conditions in terms of different types of sub manifolds of the target space. We point out how the open sigma models correspond to new types of target space geometry. For the massive Landau-Ginzburg models (both Kahler and bihermitean) we discuss an important class of supersymmetric boundary conditions which admits a nice geometrical interpretation.