$T\overline{T}$-deformed free energy of the Airy model

TL;DR

This paper investigates the effects of $Tar{T}$ deformation on the Airy model's free energy, revealing monotonic behavior at low temperatures and uncovering non-perturbative effects at all genus levels.

Contribution

It introduces a method to compute deformed correlators and free energies in the Airy model, extending understanding of $Tar{T}$ deformations beyond JT gravity.

Findings

Quenched free energy decreases monotonically with temperature at leading order.

Non-perturbative effects significantly influence the all-genus free energy.

Non-perturbative branch contributions are important under $Tar{T}$ deformation.

Abstract

Sharpening the holographic correspondence of Jackiw-Teitelboim (JT) gravity and its dual matrix model description at a finite radial cutoff $\lambda$ through the $T\overline{T}$ 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 $T\overline{T}$-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 $T\overline{T}$ deformation.