N=1 supersymmetric sigma model with boundaries, II

We consider the N = 1 supersymmetric two-dimensional nonlinear sigma model with boundaries and nonzero B-field. By analysing the appropriate currents we describe the full set of boundary conditions compatible with N = 1 superconformal symmetry. Using this result the problem of finding a correct action is discussed. We interpret the supersymmetric boundary conditions as a maximal integral submanifold of the target space manifold, and speculate about a new geometrical structure, the deformation of an almost product structure. (C) 2003 Elsevier B.V. All rights reserved.