Nonperturbative effects and resurgence in Jackiw-Teitelboim gravity at finite cutoff

We investigate the nonperturbative structure of Jackiw-Teitelboim gravity at finite cutoff, as given by its proposed formulation in terms of a T (T) over bar -deformed Schwarzian quantum mechanics. Our starting point is a careful computation of the disk partition function to all orders in the perturbative expansion in the cutoff parameter. We show that the perturbative series is asymptotic and that it admits a precise completion exploiting the analytical properties of its Borel transform, as prescribed by resurgence theory. The final result is then naturally interpreted in terms of the nonperturbative branch of the T (T) over bar -deformed spectrum. The finite-cutoff trumpet partition function is computed by applying the same strategy. In the second part of the paper, we propose an extension of this formalism to arbitrary topologies, using the basic gluing rules of the undeformed case. The Weil-Petersson integrations can be safely performed due to the nonperturbative corrections and give results that are compatible with the flow equation associated with the T (T) over bar deformation. We derive exact expressions for general topologies and show that these are captured by a suitable deformation of the Eynard-Orantin topological recursion. Finally, we study the slope and ramp regimes of the spectral form factor as functions of the cutoff parameter.

Automated summary

In this paper, we investigate the nonperturbative structure of Jackiw-Teitelboim gravity at finite cutoff by proposing a formulation in terms of a T(T) over bar -deformed Schwarzian quantum mechanics. The perturbative expansion in the cutoff parameter is computed to all orders, and it is shown to be asymptotic with a precise completion based on the analytical properties of its Borel transform. The results are interpreted in terms of the nonperturbative branch of the T(T) over bar -deformed spectrum. The extension of this formalism to arbitrary topologies is also proposed, and exact expressions for general topologies are derived using the basic gluing rules. The results are consistent with the flow equation associated with the T(T) over bar deformation. Furthermore, the spectral form factor is studied in the slope and ramp regimes as functions of the cutoff parameter.