The gravitational path integral, supersymmetry and black holes 

Davide Cassani - INFN Padova

Abstract
In a famous work, Gibbons-Hawking showed how the Euclidean gravitational path integral with suitable boundary conditions can be interpreted as a grand-canonical partition function. Solutions to the classical equations of motion, including black holes, arise as saddles of the path integral, and from the saddle-point action one can extract the conserved charges as well as the black hole entropy. In the talk, I will discuss some recent developments of these ideas. Working in five dimensions, we will see how imposing supersymmetric boundary conditions transforms the partition function into an index, what are the saddles of the index, how their on-shell action can be computed via equivariant localization and how this is related to the black hole entropy. I will also comment on how to go beyond the semiclassical regime as well as on the relevance of these developments for black hole microstate counting and holography.

You can also attend online on Zoom:

https://us02web.zoom.us/j/83556972608?pwd=RgCtoMz786nTluQDnBYvfZhH6EEXYN.1

Meeting ID: 835 5697 2608
Passcode: 073113