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Matrix Models and Deformations of JT Gravity

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arxiv 2006.13414 v1 pith:FMM6DGHB submitted 2020-06-24 hep-th

Edward Witten This is my paper · ORCID
classification hep-th
keywords matrixdualgravitymodelactionanswerbulkfrac
verification ladder T0 review T1 audit T2 compute T3 formal

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abstract

Recently, it has been found that JT gravity, which is a two-dimensional theory with bulk action $ -\frac{1}{2}\int {\mathrm d}^2x \sqrt g\phi(R+2)$, is dual to a matrix model, that is, a random ensemble of quantum systems rather than a specific quantum mechanical system. In this article, we argue that a deformation of JT gravity with bulk action $ -\frac{1}{2}\int {\mathrm d}^2x \sqrt g(\phi R+W(\phi))$ is likewise dual to a matrix model. With a specific procedure for defining the path integral of the theory, we determine the density of eigenvalues of the dual matrix model. There is a simple answer if $W(0)=0$, and otherwise a rather complicated answer.

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Cited by 5 Pith papers

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  1. An entropic puzzle in periodic dilaton gravity and DSSYK

    hep-th 2024-11 conditional novelty 8.0 of 10

    Gauging a momentum shift symmetry in sine dilaton gravity yields the DSSYK spectrum, makes negative-length states null, and predicts a finite entropy S=2πθ−2θ² instead of the Bekenstein-Hawking area law.

  2. Hollow-grams: Generalized Entanglement Wedges from the Gravitational Path Integral

    hep-th 2025-06 conditional novelty 7.0 of 10

    The entropy of a bulk region in holographic states equals the generalized entropy of the smallest wedge containing it, derived from a replica path integral via a hollow-graphic construction.

  3. A single geometry from an all-genus expansion in quantum gravity

    hep-th 2024-12 conditional novelty 7.0 of 10

    The all-genus JT gravity path integral at beta ~ e^{2S0/3} is reproduced at leading order by a disk path integral with a cubic, nonlocal dilaton interaction.

  4. Quantum gravity around ultracold black holes from DSSYK

    hep-th 2026-08 conditional novelty 6.0 of 10

    Ultracold Reissner-Nordström de Sitter black hole fluctuations are proposed to be described by a gauged near-flat dilaton gravity model with a Gaussian spectral density, yielding a finite partition function and dynami...

  5. Spread complexity and the saturation of wormhole size

    hep-th 2024-12 conditional novelty 6.0 of 10

    For finite-N DSSYK, the chord basis is the early part of the physical Krylov basis, and spread complexity, taken as the non-perturbative ER bridge size, saturates after a universality-class-dependent peak and slope.

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