Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity (1910.10311v1)

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.

Insights into Late Time Behavior in JT Gravity

The paper "Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity" by Phil Saad focuses on understanding late time correlation functions in the context of Jackiw-Teitelboim (JT) gravity, a model of two-dimensional gravity. The paper explores complex phenomena such as the discreteness of the black hole microstates and the Eigenstate Thermalization Hypothesis (ETH), using JT gravity as a theoretical underpinning.

Correlation Functions and Ensemble Averaging

The fundamental issue addressed in this paper is the behavior of correlation functions at late times in quantum systems, specifically JT gravity. In such systems, the quantum states of black holes consist of numerous microstates, indistinguishable on a macroscopic level. The late time correlation functions in these systems are significant as they probe the persistence of memory of these microstates. Saad articulates that this behavior reflects the discreteness of the energy spectrum in black hole systems, suggesting that averaged features—ramp and plateau—emerge due to random matrix statistics governing the energy levels.

Mechanistic Insights and Topological Transitions

A unique perspective provided through this paper is the integral role of topology changes due to baby universe processes in affecting JT gravity system dynamics. These processes involve baby universes—small, additional closed universes—being emitted and absorbed by the parent universe. Saad presents two primary mechanisms through which topology change implements lasting effects: "shortening" of Einstein-Rosen bridges and providing “shortcuts” for particles within the geometry of JT gravity. These topological effects are accentuated by random matrix theory statistical predictions which are seamlessly integrated into the behavior of correlation functions at late times.

Eigenstate Thermalization Hypothesis (ETH)

The Eigenstate Thermalization Hypothesis is central to interpreting the thermal behavior of black holes at late times. It posits small fluctuations among the energy eigenstates allowing correlation functions to stabilize after initially decaying. This hypothesis is crucial in framing non-decaying behaviors in systems governed by ensemble Hamiltonians, emphasizing that the ETH aligns statistical elements within JT gravity systems adequately for such predictions. Saad validates these alignments through precise predictions for both diagonal and off-diagonal matrix elements involved in such systems.

Practical and Theoretical Implications

The exploration of long time behavior in JT gravity helps bridge theoretical predictions with practical expectations in the field of quantum gravity and black hole thermodynamics. The implications of late time correlation functions in quantum systems are broad, suggesting possible universality in distinct statistical behaviors across seemingly disparate quantum models. Furthermore, the paper speculates future trajectories of such investigations, particularly in refining the connections between ETH and observable behaviors in quantum scale black holes.

Concluding Thoughts

This paper makes compelling strides in connecting traditional matrix theory predictions with novel descriptions of dynamics in JT gravity. Saad's paper also importantly speculates on the quantum behavior in black hole models with a level of coherent integration rarely achieved in such complex quantum field discussions. Future extensions of these insights might dynamically reshape our understanding of black holes and their long-term thermodynamic properties.

By providing robust verification of theoretical models with empirical expectations, this paper contributes an essential layer of depth to the field of theoretical physics and aids in fostering meaningful discussions on the broader implications of the universality of JT gravity predictions. The nuanced approach applied in evaluating random matrix statistics and ETH frameworks stands poised for broader applications across interconnected realms of quantum theory and cosmological phenomena.