Low Energy Thermodynamics of JT Gravity and Supergravity

TL;DR

This paper investigates the low energy thermodynamics of JT gravity and supergravity using non-perturbative minimal string models, revealing linear temperature dependence of entropy and specific heat at low temperatures.

Contribution

It introduces a new replica-scaling limit to analyze non-perturbative low energy physics in JT gravity and supergravity models, connecting ensemble averages with wormhole geometries.

Findings

Spectral density remains finite at zero energy.

Low temperature entropy and specific heat are linear in temperature.

Non-perturbative models exhibit consistent thermodynamic behavior.

Abstract

Aspects of the low energy physics of certain Jackiw-Teitelboim gravity and supergravity theories are explored, using their recently presented non-perturbative description in terms of minimal string models. This regime necessarily involves non-perturbative phenomena, and the inclusion of wormhole geometries connecting multiple copies of the nearly AdS$_2$ boundary in the computation of ensemble averages of key quantities. A new "replica-scaling" limit is considered, combining the replica method and double scaling with the low energy limit. Using it, the leading free energy, entropy, and specific heat are explored for various examples. Two models of particular note are the JT supergravity theory defined as a (1,2) Altland-Zirnbauer matrix ensemble by Stanford and Witten, and the Saad-Shenker-Stanford matrix model of ordinary JT gravity (non-perturbatively improved at low energy). The full models have a finite non-vanishing spectral density at zero energy. The replica-scaling construction suggests for them a low temperature entropy and specific heat that are linear in temperature.