Nonperturbative effects and resurgence in JT gravity at finite cutoff

TL;DR

This work develops a nonperturbative definition of JT gravity at finite cutoff by embedding it in a $T\bar{T}$-deformed Schwarzian framework and applying resurgence to the perturbative expansion. It derives closed-form, nonperturbatively complete disk and trumpet partition functions, demonstrates a deformed yet consistent topological recursion for arbitrary topologies, and analyzes the resulting spectrum and spectral-form-factor behavior. The findings reveal a finite-cutoff deformation that preserves flow equations while introducing nonpositive-density regions and nonperturbative instanton effects, providing a refined holographic RG picture and a nonperturbative handle on gravity in finite patches. The approach connects resurgence, topological recursion, and Weil–Petersson geometry in a unified description of JT gravity beyond perturbation theory, with implications for holography at finite volume and the interpretation of spectral statistics in gravitational ensembles.

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.

Figures (5)

• Figure 1: The disk (left) and trumpet (right) topologies. The dashed lines represent the full AdS$_2$ geometry, while the actual manifolds have wiggly boundary of length $\beta/\epsilon$. The trumpet has an additional boundary, running along a geodesic of length $b$.
• Figure 2: The lateral Borel resummations of $Z^{\text{disk}}$ and $Z^{\text{trumpet}}$ approaching the Stokes line at $\theta = 0$ from above and below.
• Figure 3: The contour $\mathfrak{S}$ surrounding the branch cut of the integrands in \ref{['EQ:Z_disk_integral']} and \ref{['EQ:Z_trumpet_integral']}.
• Figure 4: The topological decomposition of the cylinder in terms of two trumpets glued along their geodesic boundary.
• Figure 5: The topological decomposition of a disk at genus one. A trumpet is glued to genus-one Riemann surface along a common geodesic boundary.