Free energy for deformed Jackiw-Teitelboim gravity

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.

Automated summary

This paper investigates a particular deformation of the Jackiw-Teitelboim gravity studied recently by Maxfield, Turiaci, and independently by Witten, calculating the partition function and higher-order correlators in the low temperature limit for small perturbations. The results match with the Airy limit of a Hermitian random matrix ensemble. Furthermore, the study of the free energy of the model shows that although the annealed free energy has pathological behaviors, the quenched free energy evaluated by replica trick exhibits desired properties at low temperatures.