D-branes in Gepner models and supersymmetry

Boundary states corresponding to wrapped D-branes in Calabi-Yau compactifications of type II strings are discussed using Gepner models. In particular boundary conditions corresponding to D-0 branes and D-instantons in four dimensions are investigated. The boundary states constructed by Recknagel and Schomerus are analyzed in the light-cone gauge and the broken and conserved space-time supersymmetry charges are found. The geometrical interpretation of these algebraically constructed boundary states is clarified in some simple cases. Moreover, the action of mirror symmetry and other discrete symmetries of the Gepner model on the boundary states are discussed. As an application the boundary states are used to calculate instanton induced corrections to metric on the hypermultiplets in the N = 2 effective action.