Spin-Statistics for Black Hole Microstates

TL;DR

This paper develops a method using the gravitational path integral to distinguish and count bosonic and fermionic black hole microstates, providing insights into their high-energy spectrum and wormhole contributions.

Contribution

It introduces a universal rotating black hole to compute separate microstate counts via the path integral, extending analysis to non-supersymmetric holographic theories.

Findings

Separated bosonic and fermionic microstate counts obtained

Constraints on high-energy spectrum of holographic CFTs derived

Wormhole contributions to black hole microstate calculations analyzed

Abstract

The gravitational path integral can be used to compute the number of black hole states for a given energy window, or the free energy in a thermal ensemble. In this article we explain how to use the gravitational path integral to compute the separate number of bosonic and fermionic black hole microstates. We do this by comparing the partition function with and without the insertion of $(-1)^{\sf F}$. In particular we introduce a universal rotating black hole that contributes to the partition function in the presence of $(-1)^{\sf F}$. We study this problem for black holes in asymptotically flat space and in AdS, putting constraints on the high energy spectrum of holographic CFTs (not necessarily supersymmetric). Finally, we analyze wormhole contributions to related quantities.