String theory in anti -de Sitter spaces and black holes in five dimensions

In part I of this thesis we study two-dimensional sigma models on supergroup manifolds and their quotients as well as their relation with the string theory in anti-deSitter spaces. First we investigate the sigma model on the PSL(n|n) supergroup manifold. We demonstrate that this theory is exactly conformal. We show that all group invariant correlation functions are coupling constant independent and can be computed in the free theory. The non-invariant correlation functions are nontrivial and coupling dependent. We also compare two and three-point correlation functions of the PSL(1, 1|2) sigma model with the correlation functions in the boundary theory of AdS 3 × S3 and find a qualitative agreement. Then we use a PSU(1, 1|2)/U(1) × U(1) sigma model with a Wess-Zumino term to quantize the superstring theory on the AdS2 × S2 background with Ramond-Ramond flux. One-loop conformal invariance of the model is guaranteed by a general mechanism which holds for coset spaces G/H where G is Ricci-flat and H is the invariant locus of a Z4 automorphism of G. This mechanism gives one-loop conformal theories for the PSU(1, 1|2) × PSU(2|2)/ SU(2) × SU(2) and PSU(2, 2|4)/SO(4, 1) × SO(5) coset spaces, suggesting our results might be useful for quantizing the superstring on AdS3 × S3 and AdS5 × S5 backgrounds.;In part II we study extremal black holes in the context of five dimensional N = 2 supergravity. We examine the attractor mechanism for those black holes and show that attractor points are unique in the extended vector multiplet moduli space. Implications for black hole entropy and domain walls in gauged supergravity are discussed. Next we derive geometric formula for the entropy of such black holes and speculate on its possible interpretations. At the end we address a puzzle arising for black hole solutions where the moduli fields in spacetime cross into the different phase of the supergravity.