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Résumé |
Providing a microscopic derivation of the entropy of supersymmetric asymptotically AdS_5
black holes has been an open problem for 15 years. In the talk I will present progress in this
direction. On the gravity side of the AdS/CFT correspondence, I will describe a BPS limit of
black hole thermodynamics by first focussing on a supersymmetric family of complexified
solutions and then reaching extremality. In this limit the black hole entropy is the Legendre
transform of the on-shell gravitational action with respect to a set of chemical potentials
subject to a specific constraint. The latter follows from supersymmetry and regularity in the
Euclidean bulk geometry. The gravitational analysis instructs us that the dual N=1
superconformal field theory is defined on a twisted S^1 x S^3 with complexified chemical
potentials obeying the constraint, and localization allows to compute the corresponding
partition function exactly. This computation defines a generalization of the supersymmetric
Casimir energy, whose Legendre transform at large N precisely reproduces the Bekenstein-
Hawking entropy of the black hole. |
