D-BRANES ON CALABI-YAU SPACES AND THEIR MIRRORS

We study the boundary states of D-branes wrapped around supersymmetric cycles in a general Calabi-Yau manifold. In particular, we show how t he geometric data on the cycles are encoded in the boundary states, As an application, we analyze how the minor symmetry transforms D-branes , and we verify that it is consistent with the conjectured periodicity and the monodromy of the Ramond-Ramond field configuration on a Calab i-Yau manifold. This also enables us to study open string worldsheet i nstanton corrections and relate them to closed string instanton counti ng. The cases when the mirror symmetry is realized as T-duality are al so discussed.