Anti-de Sitter D-branes

We study D-branes of the SL(2, R) WZW model and of its discrete orbifolds. Gluing the currents by group automorphisms leads to three types of D-branes : two-dimensional hyperbolic planes (H-2), de Sitter branes (dS(2)), or ant i-de Sitter branes (AdS(2)). We explain that the dS(2) branes are unphysica l, because the electric field on their world-volume is supercritical. By co mbining SL(2, R) and SU(2), we exhibit a class of supersymmetric AdS(2) X S -2 three-brane world-volumes, and consider their possible embeddings in the near-horizon region of stringy black holes. We point out the intriguing di fference between the induced and the effective geometries of these D-branes , and speculate on its possible significance.