D-Branes on Group Manifolds

Possible Dirichlet boundary states for WZW models with untwisted affine super Kac-Moody symmetry are classified for all compact simple Lie groups. They are obtained by inner- and outer-automorphism of the group. D-brane world-volume turns out to be a group manifold of a symmetric subgroup, so that the moduli space of D-brane is a irreducible Riemannian symmetric space. It is also clarified how these D-branes are transformed to each other under abelian T-duality of WZW model. Our result implies, for example, there is no D-particle on the compact simple group manifold. When the D-brane world-volume contains $S^1$ factor, the D-brane moduli space becomes hermitian symmetric space and the open string world-sheet instantons are allowed.