Constructing all BPS black hole microstates from the gravitational path integral

TL;DR

The paper develops a state-by-state construction of all BPS black hole microstates using the gravitational path integral, then shows that the resulting Hilbert-space dimension precisely matches the Gibbons-Hawking degeneracy, including non-perturbative $1/G_N$ corrections. It leverages $ ext{N}=2$ super-JT gravity and multiboundary correlators to compute the rank of a mixed BPS density matrix via a resolvent method, demonstrating that wormhole contributions reproduce the GH count while higher-genus effects vanish in the BPS sector. The authors further interpret the boundary states as Gaussian Haar-random states, show a vanishing standard deviation for the rank (hence exactness), and provide an explicit reconstruction procedure to obtain arbitrary two-sided BPS states from the constructed basis. This work thus resolves a supersymmetric version of the black hole information paradox and offers a concrete, state-by-state account of BPS microstates consistent with established degeneracy counts, with potential implications for boundary algebras and dual descriptions.

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.

Figures (7)

• Figure 1: Consistency conditions for triangle and quadrilateral partition functions: (a) triangle glued to three Hartle-Hawking wavefunctions recovers the disk partition function. (b) Two triangles are glued together to obtain a quadrilateral which we glue to four Hartle-Hawking wavefunctions to recover the disk partition function.
• Figure 2: Branch-cut structure in the complex $\lambda$-plane for different values of $K$. This branch-cut gives rise to the density of eigenvalues $D(\lambda)$ shown in \ref{['eq:density-of-eigenvalues']} whose behavior we analyze in detail in the paragraph below that equation.
• Figure 3: Examples of geometries around which the supergravity path integral yields a vanishing answer. In all cases there is a closed geodesic, shown in green, that does not intersect any of the matter propagators shown in red. The first line (figure a -- c) consists of higher genus geometries. The second line (figures d -- g) contains vanishing geometries that have genus zero but decompose into more than two patches, with at least one patch not homotopic to a disk geometry.
• Figure 4: (a) A pinwheel without any defects (b) A pinwheel with one defect on the front polygon (c) A pinwheel with one defect on the back polygon (d) A pinwheel with two defects one on the front and one on the back
• Figure 5: The pink curve shows a geodesic that connects two particle insertions on the boundary (a) a matter loop that closes (b) the shortest geodesic from the matter geodesic to itself, that wraps the cylinder once but does not necessarily form a closed loop. In the calculation below, we shall use the blue geodesic in the right figure to bound the length of the closed geodesic in the left figure.