Jul 18 – 23, 2022
University of Vienna
Europe/Vienna timezone

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

Not scheduled
Audimax (University of Vienna)


University of Vienna

Universitätsring 1, 1010 Vienna, Austria


Torsten Weber (University of Regensburg)


In the last years the discovery of the duality between JT quantum gravity and a double-scaled matrix model [1] has led to an intense cross-fertilization between the fields of holography and quantum chaos. Starting on the quantum chaos side, we investigate the implications imposed by the universal RMT behaviour of the matrix model [2] on JT gravity. Specifically we show how the consistency of both sides of the duality imposes a set of constraints on the volumes of the moduli space of hyperbolic 2-manifolds for all genera. These volumes, known as Weil-Petersson volumes, are polynomial functions and can be computed using the celebrated nonlinear recursion formula due to Mirzakhani [3] which for larger genus becomes increasingly difficult to analyse. Since our results take the form of 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.

[1] P. Saad, S. Shenker, D. Stanford, arXiv:1903.11115
[2] See e.g. F. Haake, Quantum Signatures of Chaos, Springer, 2000
[3] M. Mirzakhani, Inventiones mathematicae 167.1, pp. 179-222

Primary authors

Torsten Weber (University of Regensburg) Fabian Haneder (University of Regensburg)


Prof. Juan-Diego Urbina (University of Regensburg) Prof. Klaus Richter (University of Regensburg)

Presentation materials

There are no materials yet.