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 $V_{g,n}(b_1,\dots ,b_n)$ 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 $V_{g,n}(b_1,\dots ,b_n)$ with $n$ boundaries when $g$ is large.

arXiv comment14 pages. Added references. Version to appear in Physics Letters B

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• Path integrals in JT gravity and Virasoro constraints
• Asymptotics of Weil-Petersson volumes and two-dimensional quantum gravities