Eigenstate Thermalization and Disorder Averaging in Gravity

TL;DR

The paper derives a gravity-compatible EFT for typical microstates to reproduce ETH-like correlator moments, showing disorder averaging and replica instantons emerge without invoking a fundamental ensemble of theories. By constructing generating functions for mean and higher moments, and translating them into bulk gravitational saddles, the authors map second and higher moments to microcanonical black holes and wormhole connections between replicas. Concrete examples with product CFTs and Rényi partition functions illustrate how connected correlations arise and how Rényi entropies are computed in this framework. The work clarifies the relationship between ensembles in gravity, chaos, and coarse-graining, and outlines how the EFT could be extended toward a fuller gravitational effective field theory description of information retrieval in black holes.

Abstract

Naively, a resolution of the black hole information paradox appears to involve microscopic details of a theory of quantum gravity. However, recent work has argued that a unitary Page curve can be recovered by including novel replica instantons in the gravitational path integral. Moreover, replica instantons seem to rely on disorder averaging the microscopic theory, without a definite connection to a single, underlying unitary quantum system. In this letter, we show that disorder averaging and replica instantons emerge naturally from a gravitational effective theory built out of typical microscopic states. We relate replica instantons to a moment expansion of the simple operators appearing in the Eigenstate Thermalization Hypothesis, describe Feynman rules for computing the moments, and find an elegant microcanonical description of replica instantons in terms of wormholes and Euclidean black holes.

Figures (1)

• Figure 1: Euclidean JT wormholes Penington:2019kki (top) and corresponding microcanonical wormholes (bottom).