Weber, Torsten and Haneder, Fabian and Richter, Klaus and Urbina, Juan Diego (2023) Constraining Weil-Petersson volumes by universal random matrix correlations in low-dimensional quantum gravity. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 56 (20): 205206. ISSN 1751-8113, 1751-8121
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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 (WP) volumes, solving a celebrated nonlinear recursion formula that is notoriously difficult to analyse. Since our results imply linear relations between the coefficients of the WP 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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CURVES; random matrix theory; quantum gravity; hyperbolic geometry; JT gravity; holography; quantum chaos |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics > Chair Professor Richter > Group Klaus Richter |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 22 Feb 2024 09:45 |
| Last Modified: | 22 Feb 2024 09:45 |
| URI: | https://pred.uni-regensburg.de/id/eprint/59062 |
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