JT gravity and the asymptotic Weil-Petersson volume

Abstract: A path integral in Jackiw-Teitelboim (JT) gravity is given by integrating over the volume of the moduli of Riemann surfaces with boundaries, known as the "Weil-Petersson volume," together with integrals over wiggles along the boundaries. The exact computation of the Weil-Petersson volume $V_{g,n}(b_1, \ldots, b_n)$ is difficult when the genus $g$ becomes large. We utilize two partial differential equations known to hold on the Weil-Petersson volumes to estimate asymptotic behaviors of the volume with two boundaries $V_{g,2}(b_1, b_2)$ and the volume with three boundaries $V_{g,3}(b_1, b_2, b_3)$ when the genus $g$ is large. Furthermore, we present a conjecture on the asymptotic expression for general $V_{g,n}(b_1, \ldots, b_n)$ with $n$ boundaries when $g$ is large.