The world-sheet description of A and B branes revisited

We give a manifest supersymmetric description of A and B branes on Kahler manifolds using a completely local N=2 superspace formulation of the world-sheet nonlinear sigma-model in the presence of a boundary. In particular, we show that an N=2 superspace description of type A boundaries is possible, at least when the background is Kahler. This leads to an elegant and concrete setting for studying coisotropic A branes. Here, apgesan important role is played by the boundary potential, whose precise physical meaning remains to be fully understood. Duality transformations relating A and B branes in the presence of isometries are studied as well.