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Nonperturbative effects and resurgence in JT gravity at finite cutoff
High Energy Physics - Theory · Submitted 2 Jun 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | contribution 0.92 | 0.80 | 0.06 | asserted 0.93 |
| s1 | Our starting point is a careful computation of the disk partition function to all orders in the perturbative expansion in the cutoff parameter. | method 0.93 | 0.95 | 0.03 | asserted 0.93 |
| s2 | 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. | result 0.90 | 0.94 | 0.34 | asserted 1.00 |
| s3 | The final result is then naturally interpreted in terms of the nonperturbative branch of the $T\bar{T}$-deformed spectrum. | interpretation 1.00 | 0.85 | 0.28 | asserted 0.96 |
| s4 | The finite-cutoff trumpet partition function is computed by applying the same strategy. | contribution 0.55 | 0.92 | 0.04 | asserted 1.00 |
| s5 | 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. | contribution 0.91 | 0.87 | 0.06 | asserted 0.75 |
| s6 | 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. | result 0.85 | 0.86 | 0.11 | asserted 0.81 |
| s7 | We derive exact expressions for general topologies and show that these are captured by a suitable deformation of the Eynard-Orantin topological recursion. | result 0.77 | 0.96 | 0.21 | asserted 1.00 |
| s8 | Finally, we study the "slope" and "ramp" regimes of the spectral form factor as functions of the cutoff parameter. | contribution 0.88 | 0.94 | 0.08 | asserted 0.93 |
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The paper
Original 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.
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References
How the literature uses it
27 arXiv papers cite this in 69 sentences
Papers citing it · 47 sentences without a confident label
Builds on it 1 paper
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Based on JT results [ref] Z_JT,D (u,t) =u/√(t)e^-u/t/u^2+4π^2 tI_2(1/t√(u^2+4π^2 t)) Z_JT,D (u,t) = u/√(t)e^-u/t/√(u^2-b^2t)I_1(1/t√(u^2-b^2 t)), u=2β, where $I_1,I_2$ are modified Bessel functions.
Note on $T\bar{T}$ deformed matrix models and JT supergravity duals · Gravity side · 0.80
Uses its method or tool 4 papers
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The deformed disk and trumpet partition function can be worked out by applying the techniques developed in [ref] as well as the method in [ref] .
Note on $T\bar{T}$ deformed matrix models and JT supergravity duals · Introduction · 1.00
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We study Dirichlet boundary conditions on the geometry at a finite proper distance from the horizon, following the method of York [ref] applied to the de Sitter case [ref] .[Ordinary JT gravity with Dirichlet boundary conditions was considered, for example, in [ref] .] The temperature is fixed to be the Tolman temperature [ref] , which is the proper length of the Euclidean boundary $S^1$.
Interpolating geometries and the stretched dS$_2$ horizon · Introduction · 0.90
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[equation] Now, by change of variables $R_g,n$'s are related with $W_g,n$'s in the following way [ref] , [equation] Now following [ref] , [equation]
Finite cutoff JT gravity: Baby universes, Matrix dual, and (Krylov) Complexity · $TT̅$ deformation of the volume of moduli space · 0.91
Compares with it 4 papers
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This difference is also the main lesson of our comparison with previous finite cutoff proposals [ref] .
Quantum JT Gravity in a box as a P\"oschl-Teller Scattering Problem · Introduction · 0.98
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Triple-Scaling LimitIn addition, we observe from the relative minus sign case in [ref] that the deformed chord Hamiltonian takes the same form as the canonically quantized ADM Hamiltonian of JT gravity at a finite cutoff found by [ref] (7.6) where the parameter $r_b$ in the JT gravity case corresponds to $y$ in the boundary theory [ref].
Deforming the Double-Scaled SYK & Reaching the Stretched Horizon From Finite Cutoff Holography · Krylov Spread Complexity · 0.91
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Notice that $ρ_SJT,D(E,t)$ is negative in the range $(2/t,4/t)$, which is similar with JT case [ref] .
Note on $T\bar{T}$ deformed matrix models and JT supergravity duals · Gravity side · 0.95
Cites it as support 2 papers
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We choose to keep both, as there are cases e.g. [ref] where both branches are necessary.
Massive gravity generalization of $T\overline{T}$ deformations · Spectrum analysis · 1.00
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This fact is also adopted in [ref] .
$T\overline{T}$-deformed free energy of the Airy model · $TT$ deformed correlation functions in JT gravity · 0.97
Cites it as background 9 papers
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In the present work, we are interested in the JT and SJT/ matrix model duality with $TT̅$ deformation [ref] .
Note on $T\bar{T}$ deformed matrix models and JT supergravity duals · Introduction · 0.87
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This has motivated studying higher [ref] and lower dimensional analogs/extensions [ref] ; we collectively refer to them as $T^2$ deformations[Also referred to as 1D $$ deformations in the lower-dimensional case in [ref] .].
Deforming the Double-Scaled SYK & Reaching the Stretched Horizon From Finite Cutoff Holography · Introduction · 0.82
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Recent studies of JT gravity include [ref] .
Path integrals in JT gravity and Virasoro constraints · Introduction · 0.99
What it cites · 53 sentences without a confident label
Uses the method or tool of 3 papers
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We then exploit the standard resurgence technique [ref] , using the properties of the lateral Borel resummation, to take into account nonperturbative contributions.
An Introduction to Resurgence, Trans-Series and Alien Calculus · Introduction · 1.00
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We then exploit the standard resurgence technique [ref] , using the properties of the lateral Borel resummation, to take into account nonperturbative contributions.
A Primer on Resurgent Transseries and Their Asymptotics · Introduction · 1.00
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We then applied our findings to compute results for arbitrary topologies, exploiting the gluing procedure of [ref] .
JT gravity as a matrix integral · Conclusions and outlook · 0.95
Compares with 1 paper
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Such a choice is in sharp contrast with the approach of [ref] , where instead, a significant role was played by a particular class of paths in the nonperturbative regime, leading to very different results.
Finite-cutoff JT gravity and self-avoiding loops · Conclusions and outlook · 0.87
Cites as background 9 papers
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In its modern formulation [ref] , the JT path integral itself is defined as a limit procedure from a cut-off theory: after imposing Dirichlet boundary conditions at some finite distance, the proper boundary length and the boundary value for the dilaton are scaled appropriately in the large area limit to preserve the boundary degrees of freedom.
Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space · Introduction · 0.84
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At $t=0$ [ref] , JT gravity was observed to reproduce the characteristic shape of a spectral form factor associated with an ensemble of Hamiltonians with random-matrix statistics.
JT gravity as a matrix integral · The spectral form factor · 0.83
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While there have been attempts to generalize the conjecture to higher dimensions [ref] , a simpler context, where we can accurately study the status of the proposal, is to consider the finite cutoff version of Jackiw–Teitelboim (JT) gravity [ref] .
TT deformations in general dimensions · Introduction · 0.87
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