### On the holographic origin of the Bekenstein-Hawking entropy of 1/16 BPS $AdS_5$ black holes

Providing a microscopic derivation of the entropy of supersymmetric asymptotically $AdS_5$ black holes has been an open problem for some time. In the talk I will present progress towards such a derivation. On the gravity side of the AdS/CFT correspondence, I will define a BPS limit of black hole thermodynamics by first focussing on a supersymmetric family of complexified solutions and then reaching extremality. I will show that 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 constraint. This constraint 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 $S^1 \times S^3$ 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.

**Tuesday, 5th of March 2019, 14:30, sala Wataghin**