Abstract
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 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 ρ0(E) ~ \( \sqrt{E-{E}_0} \) and ρ0(E) ~ (E − E0)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.
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Acknowledgments
I am grateful to Timothy Budd, Clifford Johnson, Bart Zonneveld and Pjotr Koster for valuable discussions and comments on a draft. In particular, Timothy Budd contributed to the analysis of the hyperbolic O(n) loop model in section 2. This work is part of the START-UP 2018 programme with project number 740.018.017, which is financed by the Dutch Research Council (NWO).
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Castro, A. Critical JT gravity. J. High Energ. Phys. 2023, 36 (2023). https://doi.org/10.1007/JHEP08(2023)036
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DOI: https://doi.org/10.1007/JHEP08(2023)036