Abstract
We investigate the nonperturbative structure of Jackiw-Teitelboim gravity at finite cutoff, as given by its proposed formulation in terms of a $T\bar{T}$-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 $T\bar{T}$-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 $T\bar{T}$ 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.
Highlights
A crucial problem in quantum gravity is the precise definition of physical observables
In the second part of the paper, we explore the construction of the deformed version of the partition functions for arbitrary topologies, using the same gluing procedure derived for the undeformed theory [20]
An essential step in our construction is the explicit evaluation of the cylinder partition function: it is closely related to the kernel necessary to engineer the Eynard– Orantin topological recursion formula [24] and is responsible for the “ramp” growth in the spectral form factor [20,25,26]
Summary
A crucial problem in quantum gravity is the precise definition of physical observables. The trumpet partition function experiences an even more dramatic modification: the nonperturbative corrections completely smooth out naïve singularity associated with the fact that the cutoff boundary could overlap with the geodesic boundary Relying on this observation, in the second part of the paper, we explore the construction of the deformed version of the partition functions for arbitrary topologies, using the same gluing procedure derived for the undeformed theory [20]. An essential step in our construction is the explicit evaluation of the cylinder partition function: it is closely related to the kernel necessary to engineer the Eynard– Orantin topological recursion formula [24] and is responsible for the “ramp” growth in the spectral form factor [20,25,26] We derive in this last perspective its late-time behavior and observe the transition between the slope and the ramp phase at finite cutoff.
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