Critical JT Gravity

In this paper, we investigate a critical behavior of JT gravity, a model of two-dimensional quantum gravity on constant negatively curved spacetimes. Our approach involves using techniques from random maps to investigate the generating function of Weil--Petersson volumes, which count random hyperbolic surfaces with defects. The defects are weighted geodesic boundaries, and criticality is reached by tuning the weights to the regime where macroscopic holes emerge in the hyperbolic surface, namely \textit{non-generic criticality}. We analyze the impact of this critical regime on some universal features, such as its density of states. We present a family of models that interpolates between systems with $\rho_0(E)\sim\sqrt{E-E_0}$ and $\rho_0(E)\sim (E-E_0)^{3/2}$, which are commonly found in models of JT gravity coupled to dynamical end-of-the-world and FZZT branes, and give a precise definition of what this phase transition means from the random geometry point of view.