An integrable road to a perturbative plateau

Blommaert, Andreas; Kruthoff, Jorrit; Yao, Shunyu

doi:10.1007/jhep04(2023)048

Cited by 20 publications

(10 citation statements)

References 91 publications

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“…In appendix C we give a review of the application of the topological recursion to the setting of JT gravity with the aim of showing how we obtained the WP volumes used for checking the cancellations we predict. A collection of these can be found in appendix D. As a last note, the same cancellations as the ones we report have been found independently using intersection theory computations in [26].…”

Section: Introductionsupporting

confidence: 85%

“…Possibly useful tools to investigate such a mechanism could be provided by intersection theory, which has been used in [26] to identify the same cancellations as we have reported in this work. Some attention has also been directed towards resonance and resurgence of the JT gravity genus expansion [52,53], though mainly at the level of the free energy, and it is not immediately clear whether such considerations could be profitably used for the questions at hand.…”

Section: Discussionmentioning

confidence: 75%

“…We thank T Mertens for illuminating discussions, and A Blommaert, D Stanford, J Kruthoff and S Yao for very helpful conversations and for sharing some of their unpublished results during preparation of [26,27]. 16 We thank Thomas Mertens for explaining this point to us.…”

Section: Acknowledgmentsmentioning

confidence: 96%

“…The present paper (and its companion [26]) follows the route depicted above. We invoke the well justified assumption that in a certain precise limit, spectral correlations computed from the exact solution of Jackiw-Teitelboim (JT) gravity are identically given by the universal RMT results.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Constraining Weil–Petersson volumes by universal random matrix correlations in low-dimensional quantum gravity

Weber

Haneder

Richter

et al. 2023

J. Phys. A: Math. Theor.

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Based on the discovery of the duality between Jackiw-Teitelboim quantum gravity and a double-scaled matrix ensemble by Saad, Shenker and Stanford in 2019, we show how consistency between the two theories in the universal Random Matrix Theory (RMT) limit imposes a set of constraints on the volumes of moduli spaces of Riemannian manifolds. These volumes are given in terms of polynomial functions, the Weil-Petersson volumes, solving a celebrated nonlinear recursion formula that is notoriously difficult to analyze. Since our results imply \textit {linear} relations between the coefficients of the Weil-Petersson volumes, they therefore provide both a stringent test for their symbolic calculation and a possible way of simplifying their construction. In this way, we propose a long-term program to improve the understanding of mathematically hard aspects concerning moduli spaces of hyperbolic manifolds by using universal RMT results as input.

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Section: Introductionsupporting

confidence: 85%

Section: Discussionmentioning

confidence: 75%

Section: Acknowledgmentsmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Constraining Weil–Petersson volumes by universal random matrix correlations in low-dimensional quantum gravity

Weber

Haneder

Richter

et al. 2023

J. Phys. A: Math. Theor.

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“…Tau-scaling limit and cancellations in the quantum volumes. Some interesting recent works [139][140][141] have investigated the perturbative sum over higher-genus contributions to the spectral form factor…”

Section: 10)mentioning

confidence: 99%

The Virasoro minimal string

Collier,

Eberhardt,

Mühlmann

et al. 2024

SciPost Phys.

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We introduce a critical string theory in two dimensions and demonstrate that this theory, viewed as two-dimensional quantum gravity on the worldsheet, is equivalent to a double-scaled matrix integral. The worldsheet theory consists of Liouville CFT with central charge c≥≥ 25 coupled to timelike Liouville CFT with central charge 26-c. The double-scaled matrix integral has as its leading density of states the universal Cardy density of primaries in a two-dimensional CFT, thus motivating the name Virasoro minimal string. The duality holds for any value of the continuous parameter cc and reduces to the JT gravity/matrix integral duality in the large central charge limit. It thus provides a precise stringy realization of JT gravity. The main observables of the Virasoro minimal string are quantum analogues of the Weil-Petersson volumes, which are computed as absolutely convergent integrals of worldsheet CFT correlators over the moduli space of Riemann surfaces. By exploiting a relation of the Virasoro minimal string to three-dimensional gravity and intersection theory on the moduli space of Riemann surfaces, we are able to give a direct derivation of the duality. We provide many checks, such as explicit numerical - and in special cases, analytic - integration of string diagrams, the identification of the CFT boundary conditions with asymptotic boundaries of the two-dimensional spacetime, and the matching between the leading non-perturbative corrections of the worldsheet theory and the matrix integral. As a byproduct, we discover natural conformal boundary conditions for timelike Liouville CFT.

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Spectral form factor in the τ-scaling limit

Sakai

2023

J. High Energ. Phys.

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We study the spectral form factor (SFF) of general topological gravity in the limit of large time and fixed temperature. It has been observed recently that in this limit, called the tau-scaling limit, the genus expansion of the SFF can be summed up and the late-time behavior of the SFF such as the ramp-plateau transition can be studied analytically. In this paper we develop a technique for the systematic computation of the higher order corrections to the SFF in the strict tau-scaling limit. We obtain the first five corrections in a closed form for the general background of topological gravity. As concrete examples, we present the results for the Airy case and Jackiw-Teitelboim gravity. We find that the above higher order corrections are the Fourier transforms of the corrections to the sine-kernel approximation of the Christoffel-Darboux kernel in the dual double-scaled matrix integral, which naturally explains their structure. Along the way we also develop a technique for the systematic computation of the corrections to the sine-kernel formula, which have not been fully explored in the literature before.

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An integrable road to a perturbative plateau

Cited by 20 publications

References 91 publications

Constraining Weil–Petersson volumes by universal random matrix correlations in low-dimensional quantum gravity

Constraining Weil–Petersson volumes by universal random matrix correlations in low-dimensional quantum gravity

The Virasoro minimal string

Spectral form factor in the τ-scaling limit

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