Geometry of D-branes for general N=(2,2) sigma models
  We give a world-sheet description of D-brane in terms of gluing conditions on T+T^*. Using the notion of generalized Kahler geometry we show that A- and B-types D-branes for the general N=(2,2) supersymmetric sigma model (including a non-trivial NS-flux) correspond to the (twisted) generalized complex submanifolds with respect to the different (twisted) generalized complex structures however. 
Maxim Zabzine