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arXiv · 2202.03454

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

Stephen Ebert·Hao-Yu Sun·Zhengdi Sun
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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.

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Stephen Ebert, Hao-Yu Sun, Zhengdi Sun. 2022-02-07. $T\overline{T}$-deformed free energy of the Airy model. https://doi.org/10.1007/jhep08(2022)026

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