Constructing all BPS black hole microstates from the gravitational path integral

TL;DR

This paper demonstrates how the gravitational path integral can be used to explicitly construct and count all BPS black hole microstates, matching string theory predictions including non-perturbative effects.

Contribution

It provides a method to prepare a basis for BPS black hole microstates using the gravitational path integral, achieving an exact count consistent with string theory.

Findings

Hilbert space basis for BPS microstates constructed

Exact microstate count matches Gibbons-Hawking degeneracy

Includes all non-perturbative $1/G_N$ corrections

Abstract

Understanding how to prepare and count black hole micro-states by using the gravitational path integral is one of the most important problems in quantum gravity. Nevertheless, a state-by-state count of black hole microstates is difficult because the apparent number of degrees of freedom available in the gravitational effective theory can vastly exceed the entropy of the black hole, even in the special case of BPS black holes. In this paper, we show that we can use the gravitational path integral to prepare a basis for the Hilbert space of all BPS black hole microstates. We find that the dimension of this Hilbert space computed by an explicit state count is in complete agreement with the degeneracy obtained from the Gibbons-Hawking prescription. Specifically, this match includes all non-perturbative corrections in $1/G_N$. Such corrections are, in turn, necessary in order for this degeneracy of BPS states to match the non-perturbative terms in the $1/G_N$ expansion in the string theory count of such microstates.