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Constraining Weil–Petersson volumes by universal random matrix correlations in low-dimensional quantum gravity by Torsten Weber; Fabian Haneder; Klaus Richter; Juan Diego Urbina is a Physics and Astronomy article available to read on EtoBox.

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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 \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.

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

Author

Torsten Weber; Fabian Haneder; Klaus Richter; Juan Diego Urbina

Publisher

IOP Publishing

Published

2023

Language

EN

Field

Physics and Astronomy (Physical Sciences)