Abstract:
In recent years, the Euclidean gravitational path integral has proven to be a reliable tool for studying quantum mechanical aspects of black holes. An important quantity that can help us probe whether black holes behave like conventional quantum mechanical systems is the supersymmetric index computed directly from the gravitational path integral. In this talk, I will discuss the issue of multicentered black hole contributions to the Euclidean path integral that computes the supersymmetric index at finite temperature. In the context of Einstein-Maxwell theory in 4d, I will explain how the multicentered generalization of the Kerr-Newman black hole, called the Israel-Wilson solution, can be seen to satisfy the boundary conditions of the supersymmetric index and yields a regular contribution to the index. I will show how even though we perform the computations at finite temperature, the construction makes the value of the on-shell action depend only on the black hole charges, which can be viewed as a new form of the attractor mechanism. Finally, I will describe how we can extend the analysis to the most general solutions of N=2 4d supergravity, where the on-shell action becomes independent of the boundary values of the scalars. Time permitting, I will describe how the phenomenon of wall-crossing, in which the index jumps discontinuously as one crosses a codimension one wall in the space of asymptotic scalar moduli, arises from the perspective of the new finite temperature saddles. Based on 2310.07763 and 2501.17909 with Roberto Emparan, Luca Iliesiu, Sameer Murthy, and Joaquin Turiaci.