T(T)over-bar-deformed free energy of the Airy model

Sharpening the correspondence of Jackiw-Teitelboim (JT) gravity and its dual matrix model description at a finite radial cutoff A through the T (T) over bar deformation is of interest. To proceed, we simplify the problem by considering the Airy model and deform Airy correlators in the same way as in T (T) over bar -deformed JT gravity. We use those correlators to compute the annealed and quenched free energies for both lambda > 0 and lambda < 0 from an integral representation of the replica trick. At the leading order in lambda and low temperatures, we confirm that the genus-zero quenched free energy monotonically decreases as a function of temperature when perturbation theory is valid. We then study the all-genus quenched free energy at low temperatures, where we discover and discuss subtleties due to non-perturbative effects in the Airy model, as well as the contributions from the non-perturbative branch under the T<(T)over bar> deformation.

Automated summary

This study focuses on sharpening the correspondence between Jackiw-Teitelboim (JT) gravity and its dual matrix model description at a finite radial cutoff A through the T (T) over bar deformation. By computing the annealed and quenched free energies of the Airy model using correlators, we find that the genus-zero quenched free energy decreases monotonically as temperature increases in perturbation theory. We also explore the all-genus quenched free energy at low temperatures, uncovering subtleties arising from non-perturbative effects in the Airy model and the contributions from the non-perturbative branch under the T<(T)over bar> deformation.