On Free Energy for Deformed JT Gravity

TL;DR

This paper analyzes a deformation of JT gravity, computing its partition function and correlators, and explores its free energy behavior, revealing insights into quenched and annealed free energies at low temperatures.

Contribution

It provides an exact computation of the partition function and correlators for a deformed JT gravity model, connecting it to random matrix theory and analyzing free energy properties.

Findings

Partition function computed to all orders in genus expansion.

At low temperatures, results match Airy limit of Hermitian matrix ensemble.

Quenched free energy exhibits desired properties despite pathological annealed free energy.

Abstract

In this paper, we study a particular deformation of the Jackiw-Teitelboim gravity recently considered by Maxfield, Turiaci and independently by Witten. We will compute the partition function of this model as well as its higher order correlators to all orders in genus expansion in the low temperature limit for small perturbations. In this limit, the results match with those obtained from the Airy limit of a Hermitian random matrix ensemble. Using this result, we will also study the free energy of the model. One observes that although the annealed free energy has pathological behaviors, under certain assumptions, the quenched free energy evaluated by replica trick exhibits the desired properties at low temperatures.