Low-temperature entropy in JT gravity

Abstract

Abstract For ensembles of Hamiltonians that fall under the Dyson classification of random matrices with β ∈ {1, 2, 4}, the low-temperature mean entropy can be shown to vanish as 〈S(T)〉 ∼ κTβ + 1. A similar relation holds for Altland-Zirnbauer ensembles. JT gravity has been shown to be dual to the double-scaling limit of a β = 2 ensemble, with a classical eigenvalue density $$ \propto {e}^{S_0}\sqrt{E} $$ ∝ e S 0 E when 0 < E ≪ 1. We use universal results about the distribution of the smallest eigenvalues in such ensembles to calculate κ up to corrections that we argue are doubly exponentially small in S0.