Lectures on Branes, Black Holes, and Anti-de Sitter Space

Abstract

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 M2-, D3- and M5-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 AdS4, AdS5 and AdS7 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 nonlinear Kaluza-Klein ansatzs describing the embeddings of the U(1)4, U(1)3 and U(1)2 truncations of these supergravities, which admit 4-charge AdS4, 3-charge AdS5 and 2-charge AdS7 black hole solutions. These enable us to embed the black hole solutions back in ten and eleven dimensions and reinterpret them as M2-, D3- and M5-branes spinning in the transverse dimensions with the black hole charges given by the angular momenta of the braves. A comprehensive Appendix lists the field equations, symmetries and transformation rules of D = 11 supergravity, Type IIB supergravity, and the M2-, D3- and M5- branes.