Wormholes and black hole microstates in AdS/CFT

TL;DR

This paper proposes that Euclidean wormholes in AdS/CFT describe the coarse-grained energy level statistics of black hole microstates, linking gravitational instantons to quantum spectral properties and addressing factorization issues.

Contribution

It introduces a new interpretation of Euclidean wormholes as representing microstate energy level statistics in AdS/CFT, using constrained instantons and saddle-point analysis.

Findings

Wormhole amplitudes relate to microstate level repulsion.

The double cone geometry dominates the integral transformation.

Brane nucleation instabilities are lifted in the Lorentzian continuation.

Abstract

It has long been known that the coarse-grained approximation to the black hole density of states can be computed using classical Euclidean gravity. In this work we argue for another entry in the dictionary between Euclidean gravity and black hole physics, namely that Euclidean wormholes describe a coarse-grained approximation to the energy level statistics of black hole microstates. To do so we use the method of constrained instantons to obtain an integral representation of wormhole amplitudes in Einstein gravity and in full-fledged AdS/CFT. These amplitudes are non-perturbative corrections to the two-boundary problem in AdS quantum gravity. The full amplitude is likely UV sensitive, dominated by small wormholes, but we show it admits an integral transformation with a macroscopic, weakly curved saddle-point approximation. The saddle is the "double cone" geometry of Saad, Shenker, and Stanford, with fixed moduli. In the boundary description this saddle appears to dominate a smeared version of the connected two-point function of the black hole density of states, and suggests level repulsion in the microstate spectrum. Using these methods we further study Euclidean wormholes in pure Einstein gravity and in IIB supergravity on Euclidean AdS$_5\times\mathbb{S}^5$. We address the perturbative stability of these backgrounds and study brane nucleation instabilities in 10d supergravity. In particular, brane nucleation instabilities of the Euclidean wormholes are lifted by the analytic continuation required to obtain the Lorentzian spectral form factor from gravity. Our results indicate a factorization paradox in AdS/CFT.