Speaker
Description
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
