Lecture 3 of the Infosys-ICTS String theory lecture series
The ability to explain the entropy of supersymmetric black holes from a microscopic, statistical viewpoint is an important test of any theory of quantum gravity. I will review recent progress on this problem in the context of the AdS/CFT correspondence. Focussing on AdS5/CFT4, I will show how the entropy of supersymmetric black holes in Anti de Sitter space is counted in the microcanonical ensemble by the superconformal index of four-dimensional superconformal field theory at large N. In the grand-canonical ensemble, the supersymmetric black hole solution is identified as a saddle-point of the matrix integral representing the superconformal index. I will discuss how this is generalized to an infinite family of solutions/saddle-points with competing free energies, which leads to an intricate phase structure of the theory. Time permitting, I will discuss a third interpretation of the superconformal index as an expansion in terms of determinants/giant gravitons.
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Recordings of past talks can be found here: www.youtube.com/channel/UCw9LdPQ5t7Q7muD0qzn70TA