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

Abstract

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 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.

25 pages, matches the published version, additional clarifications and comments added as well as appendices improving the level of self-containedness

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Cited by in corpus (6)

• The Virasoro Minimal String
• Late time behavior of $n$-point spectral form factors in Airy and JT gravities
• Chaos and moduli space volumes in unorientable JT gravity
• Unorientable topological gravity and orthogonal random matrix universality
• Topological gravity for arbitrary Dyson index
• Beyond the ensemble paradigm in low dimensional quantum gravity: Schwarzian density, quantum chaos and wormhole contributions