GRASS Seminar: Supersymmetric black holes and the gravitational path integral

The semi-classical contribution of black holes to the grand-canonical partition function of gravity is obtained by evaluating their Euclidean on-shell action. This follows from the well-known fact that the partition function can be computed via the Euclidean path integral with periodic boundary conditions for the fields. These boundary conditions include a periodic identification of the Euclidean time coordinate, with period equal to the inverse temperature of the black hole. This is in tension with the fact that supersymmetric black holes are also extremal, prompting several key questions: Do supersymmetric black holes contribute to the Euclidean path integral? What are the associated saddles? The aim of this talk is to answer these questions, focusing on asymptotically-flat black hole solutions of N=2 supergravity in five dimensions. I will also discuss how to compute their on-shell action using the Berline-Vergne-Atiyah-Bott fixed-point formula in equivariant cohomology. 

Este seminario es parte del proyecto de I+D+i con referencia CEX2020-001007-S, financiado por MCIN/AEI/ 10.13039/501100011033)