The Distribution of Ground State Energies in JT Gravity

Autor:	Johnson, Clifford V.
Rok vydání:	2022
Předmět:	High Energy Physics - Theory General Relativity and Quantum Cosmology
Druh dokumentu:	Working Paper
Popis:	It is shown that the distribution of the lowest energy eigenvalue of the quantum completions of Jackiw-Teitelboim gravity is completely described by a non-linear ordinary differential equation (ODE) arising from a non-perturbative treatment of a special random Hermitian matrix model. Its solution matches the result recently obtained by computing a Fredholm determinant using quadrature methods. The new ODE approach allows for analytical expressions for the asymptotic behaviour to be extracted. The results are highly analogous to the well-known Tracy-Widom distribution for the lowest eigenvalue of Gaussian random Hermitian matrices, which appears in a very diverse set of physical and mathematical contexts. Similarly, it is expected that the new distribution characterizes a type of universality that can arise in various gravity settings, including black hole physics in various dimensions, and perhaps beyond. It has an association to a special multicritical generalization of the Gross-Witten-Wadia phase transition. Comment: 4 pages, 2 figures (plus Supplemental Material with 5 figures)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2206.00692 Zobrazit plný text záznamu View this record from Arxiv