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 Vg,n(b1,…,bn) 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 Vg,2(b1,b2) and the volume with three boundaries Vg,3(b1,b2,b3) when the genus g is large. Furthermore, we present a conjecture on the asymptotic expression for general Vg,n(b1,…,bn) with n boundaries when g is large.