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arXiv · 2208.13802

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

Torsten Weber·Fabian Haneder·Klaus Richter·Juan Diego Urbina
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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.

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Torsten Weber, Fabian Haneder, Klaus Richter, Juan Diego Urbina. 2022-08-29. Constraining Weil-Petersson volumes by universal random matrix correlations in low-dimensional quantum gravity. https://doi.org/10.1088/1751-8121/acc8a5

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