Tasi Lectures on Branes , Black Holes and Anti - De Sitter Space

In the light of the duality between physics in the bulk of anti-de Sitter space and a conformal field theory on the boundary, we review the M 2, D3 and M 5 branes and how their near-horizon geometry yields the compactification of D = 11 supergravity on S 7 , Type IIB supergravity on S 5 and D = 11 supergravity on S 4 , respectively. We discuss the " Membrane at the End of the Universe " idea and its relation to the corresponding superconformal singleton theories that live on the boundary of the AdS 4 , AdS 5 and AdS 7 vacua. The massless sectors of these compactifications are described by the maximally supersymmetric D = 4, D = 5 and D = 7 gauged supergravities. We construct the non-linear Kaluza-Klein ansätze describing the embeddings of the U (1) 4 , U (1) 3 and U (1) 2 truncations of these supergravities, which admit 4-charge AdS 4 , 3-charge AdS 5 and 2-charge AdS 7 black hole solutions. These enable us to embed the black hole solutions back in ten and eleven dimensions and reinterpret them as M 2, D3 and M 5 branes spinning in the transverse dimensions with the black hole charges given by the angular momenta of the branes. A comprehensive Appendix lists the field equations, symmetries and transformation rules of D = 11 supergravity, Type IIB supergravity, and the M 2, D3 and M 5 branes.