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

TL;DR

This paper reviews the duality between anti-de Sitter space physics and boundary conformal field theories, focusing on branes, supergravity compactifications, and black hole solutions within the AdS/CFT framework.

Contribution

It constructs explicit non-linear Kaluza-Klein ans"atze for supergravity truncations and embeds black hole solutions as spinning branes, linking lower-dimensional solutions to higher-dimensional origins.

Findings

Embedded black hole solutions as spinning branes with angular momenta.

Constructed explicit Kaluza-Klein truncations for supergravity theories.

Reinterpreted black holes in AdS as branes with specific angular momenta.

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 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 ans\"atze 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 M2, D3 and M5 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 M2, D3 and M5 branes.