Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity

By Phil Saad. 2019

202 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/78e4cd341de9a403c3eb2a0c835ac2feffdf1e74

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In Astronomy and Astrophysics

1. D. Stanford
2. J. Maldacena
3. R. Myers
4. S. Shenker
5. S. Raju
6. D. Harlow
7. Thomas Hartman
8. G. Turiaci

In Nuclear and High Energy Physics

1. D. Stanford
2. R. Myers
3. S. Raju
4. J. Maldacena
5. S. Shenker
6. D. Harlow
7. Zhenbin Yang
8. Thomas Hartman

In Statistical and Nonlinear Physics

1. D. Stanford
2. S. Raju
3. R. Myers
4. J. Maldacena
5. S. Shenker
6. Thomas Hartman
7. Zhenbin Yang
8. H. Chen

Citations in the corpus

• Entanglement islands in higher dimensions (2019, background): “Increasing the dimensionality of the setup of section 4 of [15] is a significant step forward because a possible criticism of [13–15] is that the explicit computations were only done in 2d AdS-JT gravity [26–29], which is known to be dual to an ensemble of Hamiltonians, rather than a single fixed Ha”
• Replica wormholes and the entropy of Hawking radiation (2019, background): “But more recently the work of [34, 35], as well as the present discussion, and [31], suggests that the opposite is true.”
• Random statistics of OPE coefficients and Euclidean wormholes (2020, background): “Similar observations related to connected contribution have been made in JT gravity [32].”
• Quantum extremal islands made easy. Part II. Black holes on the brane (2020, methodology): “, calculations of Renyi entropies [41, 50], the spectral form factor [122, 125], correlation functions [90, 126], and overlap of black hole microstate wavefunctions [41, 50].”
• Replica wormholes and the black hole interior (2019, methodology): “Fortunately, as argued in [58, 26], any boundary segment of length β′ m can be replaced in the JT gravity calculations by the insertion of the Wheeler-de Witt wavefunction at the homologous, non-selfintersecting bulk geodesic χ.”
• The path integral of 3D gravity near extremality; or, JT gravity with defects as a matrix integral (2020, background): “Such results provide us with the opportunity of a window into the statistics of chaotic quantum systems [69, 70, 71, 68].”