JT gravity and the ensembles of random matrix theory

By D. Stanford, E. Witten. Advances in Theoretical and Mathematical Physics, 2019

309 citations recorded by the source corpus.

We generalize the recently discovered relationship between JT gravity and double-scaled random matrix theory to the case that the boundary theory may have time-reversal symmetry and may have fermions with or without supersymmetry. The matching between variants of JT gravity and matrix ensembles depends on the assumed symmetries. Time-reversal symmetry in the boundary theory means that unorientable spacetimes must be considered in the bulk. In such a case, the partition function of JT gravity is still related to the volume of the moduli space of conformal structures, but this volume has a quantum correction and has to be computed using Reidemeister-Ray-Singer "torsion." Presence of fermions in the boundary theory (and thus a symmetry $(-1)^F$) means that the bulk has a spin or pin structure. Supersymmetry in the boundary means that the bulk theory is associated to JT supergravity and is related to the volume of the moduli space of super Riemann surfaces rather than of ordinary Riemann surfaces. In all cases we match JT gravity or supergravity with an appropriate random matrix ensemble. All ten standard random matrix ensembles make an appearance -- the three Dyson ensembles and the seven Altland-Zirnbauer ensembles. To facilitate the analysis, we extend to the other ensembles techniques that are most familiar in the case of the original Wigner-Dyson ensemble of hermitian matrices. We also generalize Mirzakhani's recursion for the volumes of ordinary moduli space to the case of super Riemann surfaces.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5a4776f07b05aab87b97300a2cb745ac15cb0969

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Citations in the corpus

AdS3 gravity and random CFT (2020, methodology): “l consider the late-time behavior of the spectral form factor, whose behavior depends on the symmetry class. For a recent discussion in the relevant context of double-scaled random matrix theory, see [55]. Suppose that we envision AdS 3 gravity as being dual to an ensemble of CFTs, inducing an ensem”
The path integral of 3D gravity near extremality; or, JT gravity with defects as a matrix integral (2020, background): “The nonperturbative path integral of JT gravity was solved recently by Saad, Shenker and Stanford [7] (see also [31]) in a genus expansion, and we directly generalize their approach to an expansion in both genus g and number of defects k.”
Quantum chaos and the complexity of spread of states (2022, unknown): “[39] Stanford, Douglas and Witten, Edward, “JT gravity and the ensembles of random matrix theory,” Adv.”
The statistical mechanics of near-BPS black holes (2020, background): “The same time-reversal properties are also true in the N = 1 theory [70].”
Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity (2019, background): “(24)In certain generalizations of JT gravity, described by other random matrix ensembles [46], these corrections are related to contributions from non-orientable geometries.”