Worldsheet approaches to D-branes on supersymmetric cycles

We consider D-branes wrapped around supersymmetric cycles of Calabi–Yau manifolds from the viewpoint of N=2 Landau–Ginzburg models with boundary as well as by consideration of boundary states in the corresponding Gepner models. The Landau–Ginzburg approach enables us to provide a target space interpretation for the boundary states. The boundary states are obtained by applying Cardy's procedure to combinations of characters in the Gepner models which are invariant under spectral flow. We are able to relate the two descriptions using common discrete symmetries occurring in the two descriptions. We thus provide an extension to the boundary, the bulk correspondence between Landau–Ginzburg orbifolds and the corresponding Gepner models.