[Paper Review] Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity

Phil Saad|arXiv (Cornell University)|Oct 23, 2019

Black Holes and Theoretical PhysicsPhysics and Astronomy88 references99 citations

TL;DR

The paper demonstrates that JT gravity coupled to matter reproduces late-time correlator behavior consistent with an ensemble of Hamiltonians with random matrix statistics and ETH, via topology-change effects from baby universes. It provides precise ramp and plateau predictions for two-point and four-point functions and interprets them through bulk Hilbert space and baby universe mechanisms.

ABSTRACT

Quantum black holes are described by a large number of macroscopically indistinguishable microstates. Correlation functions of fields outside the horizon at long time separation probe this indistinguishability. The simplest of these, the thermal two-point function, oscillates erratically around a nonperturbatively small average "ramp" and "plateau" after an initial period of decay; these non-decaying averaged features are signatures of the discreteness of the black hole spectrum. For a theory described by an ensemble of Hamiltonians, the two-point function follows this averaged behavior. In this paper we study certain correlation functions in Jackiw-Teitelboim (JT) gravity and find precise agreement with the behavior expected for a theory described by an ensemble of Hamiltonians with random matrix statistics -- the eigenstates obey the Eigenstate Thermalization Hypothesis (ETH) and the energy levels have random matrix level statistics. A central aspect of our analysis is an averaged bulk Hilbert space description of the relevant behavior. The mechanism behind this behavior is topology change due the the emission and absorption of closed "baby universes". These baby universe effects give two complementary pictures of the non-decaying behavior, related by different continuations of a Euclidean geometry. A long Einstein-Rosen bridge can become short by emitting a large baby universe, and baby universes emitted and reabsorbed at points widely separated in space and time creates a "shortcut", allowing particles to leave the interior of the black hole.

Motivation & Objective

• Motivate the study of late-time correlation functions as probes of black hole microstate indistinguishability.
• Predict late-time behavior of two-point and some OTOCs in JT gravity assuming ensemble/ETH/RMT statistics.
• Explain the role of baby universes and topology change in generating non-decaying late-time behavior.
• Provide a bulk Hilbert space formulation and connect Euclidean wormholes to late-time ramps and plateaus.

Proposed method

• Model JT gravity coupled to a free scalar as an ensemble-averaged theory with random-matrix-type statistics.
• Express late-time correlators as sums over energy eigenstates with ETH-structured matrix elements.
• Compute ramp contributions from Euclidean geometries with a handle on a disk (baby universe emission/absorption).
• Relate ramp/plateau phenomena to spectral form factor analyses and to baby-universe emission amplitudes.
• Use a bulk Hilbert space (third-quantized JT gravity) to interpret shortening and shortcut pictures of correlator behavior.
• Provide Euclidean-to-Lorentzian analytic continuations to obtain late-time two-point and four-point functions.

Experimental results

Research questions

• RQ1 Do JT gravity correlators at late times exhibit ramp and plateau behavior consistent with random-matrix statistics and ETH?
• RQ2 How do baby universes and topology change produce non-decaying late-time contributions to two-point and OTOCs?
• RQ3 Can the late-time behavior be derived from an averaged bulk Hilbert space and match ensemble predictions?
• RQ4 What is the precise bulk geometric interpretation (shortening vs. shortcuts) of the ramp in correlators?

Key findings

• Late-time two-point and four-point functions in JT gravity show ramp and plateau structures predicted by ensemble averaging and ETH.
• The ramp arises from geometries with one handle (baby-universe emission/absorption) and matches ETH/RMT expectations.
• Plateaus for correlators correspond to contributions where baby universes end in a D-brane-like state, agreeing with spectral form factor plateaus.
• A bulk Hilbert-space description (third-quantized JT gravity) accommodates the observed late-time behavior via topology change.
• Two complementary pictures of non-decaying behavior (shortening and shortcuts) are linked by Euclidean analytic continuations.
• Results extend to higher-point OTOCs, with ramp predictions for the two-handled geometry and potential for k-handled generalizations.