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

Abstract

Abstract Sharpening the correspondence of Jackiw-Teitelboim (JT) gravity and its dual matrix model description at a finite radial cutoff λ through the $$ T\overline{T} $$ T 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 $$ T\overline{T} $$ T T ¯ -deformed JT gravity. We use those correlators to compute the annealed and quenched free energies for both λ > 0 and λ < 0 from an integral representation of the replica trick. At the leading order in λ 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 $$ T\overline{T} $$ T T ¯ deformation.