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Liouville quantum gravity -- holography, JT and matrices

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arxiv 2006.07072 v5 pith:KGM3PY47 submitted 2020-06-12 hep-th

classification hep-th
keywords gravitybulkquantumtheoryboundarycorrelatorsdeformationdilaton
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. We find explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk. Their structure has a striking resemblance with observables in 2d BF (plus a boundary term), associated to a quantum deformation of $SL(2,\mathbb{R})$, a connection we develop in some detail. For the case of the $(2,p)$ minimal string theory, we compare and match the results from the continuum approach with a matrix model calculation, and verify that in the large $p$ limit the correlators match with Jackiw-Teitelboim gravity. We consider multi-boundary amplitudes that we write in terms of gluing bulk one-point functions using a quantum deformation of the Weil-Petersson volumes and gluing measures. Generating functions for genus zero Weil-Petersson volumes are derived, taking the large $p$ limit. Finally, we present preliminary evidence that the bulk theory can be interpreted as a 2d dilaton gravity model with a $\sinh \Phi$ dilaton potential.

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Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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    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.

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    hep-th 2024-12 conditional novelty 7.0 of 10

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    hep-th 2025-07 conditional novelty 6.0 of 10

    The probe-regime two-point function of sinh dilaton gravity matches the q-deformed Ward identity correlator, indicating an emergent quantum hyperbolic disk with SLq(2) isometry near the holographic boundary.

  5. $x-y$ swap for $(2,2p+1)$ minimal string

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    An x-y swapped spectral curve is conjectured to reproduce (2,2p+1) minimal string tachyon correlators without resonance transformations; verified at low genus, with a ground-ring extension that does not match HEM.

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    The one-loop gravitational path integral of sine-dilaton gravity reproduces the one-loop corrections of double-scaled SYK for the free energy (up to an ordering ambiguity) and exactly for the matter two-point function.

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