JT gravity as a matrix integral

By Phil Saad, S. Shenker, D. Stanford. 2019

708 citations recorded by the source corpus.

We present exact results for partition functions of Jackiw-Teitelboim (JT) gravity on two-dimensional surfaces of arbitrary genus with an arbitrary number of boundaries. The boundaries are of the type relevant in the NAdS${}_2$/NCFT${}_1$ correspondence. We show that the partition functions correspond to the genus expansion of a certain matrix integral. A key fact is that Mirzakhani's recursion relation for Weil-Petersson volumes maps directly onto the Eynard-Orantin "topological recursion" formulation of the loop equations for this matrix integral. The matrix integral provides a (non-unique) nonperturbative completion of the genus expansion, sensitive to the underlying discreteness of the matrix eigenvalues. In matrix integral descriptions of noncritical strings, such effects are due to an infinite number of disconnected worldsheets connected to D-branes. In JT gravity, these effects can be reproduced by a sum over an infinite number of disconnected geometries -- a type of D-brane logic applied to spacetime.

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

View Paper: https://www.semanticscholar.org/paper/a0dcd5bd0dfdebccda30e5569cb089b268965d4e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

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

In Statistical and Nonlinear Physics

1. D. Stanford
2. S. Raju
3. R. Myers
4. S. Shenker
5. J. Maldacena
6. K. Jensen
7. Thomas Hartman
8. Phil Saad

Citations in the corpus

• A Note On Complex Spacetime Metrics (2021, neutral): “Similar behavior can occur in gravity; see for example [16].”
• Operator complexity: a journey to the edge of Krylov space (2020, background): “The putative bulk realization of K-complexity should therefore be sensitive to bulk Euclidean wormholes and baby universes [37], in ensemble-averaged systems, such as SYK, as well as in individual quantum chaotic systems, as has been emphasized in [17].”
• Quantum chaos and the complexity of spread of states (2022, neutral): “In holographic theories, the partition function and the energy moments have simple geometric duals, and, at least in 2d gravity [38–43], there are non-perturbative defini-tions of these quantities.”
• The statistical mechanics of near-BPS black holes (2020, methodology): “We will follow the steps outlined in [64] (explained also recently in [63]) in non-supersymmetric JT gravity and will obtain results similar to [65], which studied boundary conditions in JT supergravity with an OSp(2,N ) isometry group.”
• Two dimensional nearly de Sitter gravity (2019, neutral): “In [26] a possible completion was chosen.”
• 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”
• Low-dimensional de Sitter quantum gravity (2019, methodology): “ global nearly dS 2 geometries as prototypes. With this analytic continuation in hand, we can relate the higher genus contributions to the nearly dS 2 path integral to the recent Euclidean results of [21], which we do in the next Section. 2.1 Basic solutions To begin, let us write down the basic sol”
• AdS3 gravity and random CFT (2020, methodology): “exist as consistent quantum mechanical models. It has recently been demonstrated that Jackiw-Teitelboim (JT) gravity [1{6], a twodimensional model of dilaton gravity, is just such a consistent theory [7]. Moreover, as one expects for consistent theories of AdS quantum gravity, it has a holographic d”
• Replica wormholes and the entropy of Hawking radiation (2019, methodology): “In contrast with [34], we are not doing the full path integral, we are simply using a saddle point approximation, so the JT gravity plus CFT only needs to be valid around these saddles.”
• Random statistics of OPE coefficients and Euclidean wormholes (2020, background): “Finally, we would like to comment on theories which require disorder averaging such as the SYK model or the dual of JT gravity, as well as their connections to Euclidean wormholes (see for example [19]).”
• The statistical mechanics of near-extremal black holes (2020, methodology): “The Euclidean path integral of such an effective theory can be computed exactly by first integrating out the gauge degrees [17, 18] and then by analyzing the boundary modes [19] of the resulting model using the well-studied Schwarzian theory [20–34].”
• A semiclassical ramp in SYK and in gravity (2018, neutral): “1 of [46] for further comments.”
• Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity (2019, methodology): “Much of this section will be a discussion of results from [21, 14, 29], rephrased in a Hilbert space language.”
• Quantum extremal islands made easy. Part II. Black holes on the brane (2020, methodology): “For example, JT gravity emerges as the low energy effective description of the SYK model [118–121], or has a definition in terms of a matrix model [122].”
• Replica wormholes and the black hole interior (2019, methodology): “We can therefore hope to make contact with the arguments from [25] for evaluating products of partition functions, in this ensemble of Hamiltonians, using bulk JT gravity path integrals.”
• Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information (2020, methodology): “ional gravity. Indeed, the model described in section3.1is plausibly the simplest possible such theory. Our models are inspired by recent work studying spacetimes of nontrivial topology in JT gravity [62,86,87], along with the addition of ‘end-of-the-world brane’ dynamical boundaries [49]. We furthe”
• Islands in de Sitter space (2020, methodology): “es the deviations away from extremality. Two dimensional de Sitter JT gravity has been studied recently [35,36] as part of recent general developments concerning the information paradox in 2d gravity [22,37,38]. The equation of motion for the metric is obtained by varying the action (2.7) with respe”
• The path integral of 3D gravity near extremality; or, JT gravity with defects as a matrix integral (2020, methodology): “For multiple boundaries, the result matches precisely what is required for a matrix integral dual generalizing [7].”