Quantum JT Gravity in a box as a Pöschl-Teller Scattering Problem
Abstract
We present a canonical quantization of Jackiw--Teitelboim gravity with finite Dirichlet boundary conditions, using the geodesic length between the two boundaries and its conjugate momentum as reduced phase space variables. The dynamics is recast as the scattering problem of a nonrelativistic particle in a repulsive Pöschl-Teller potential, naturally embedded within a hyperbolic reduction of the sl(2,ℝ) Casimir. We obtain exact wavefunctions of the universe and the disk partition function, interpreted as a transition matrix element between states of vanishing bare length. In the asymptotic limit, the theory reduces to Liouville quantum mechanics and reproduces the standard Schwarzian spectral density. At finite cutoff, however, the spectral measure exhibits genuinely nonperturbative corrections, absent in existing TT̅ approaches. These contributions admit an interpretation in terms of pinched disk geometries and are responsible for a controlled violation of the Wheeler-DeWitt equation. We also obtain closed form expressions for thermal two-point functions in terms of Wilson functions and propose diagrammatic rules for time- and out-of-time-ordered four-point functions. We further address the issue of the branch cut singularity of the quasi-local energy and propose a UV completion of the model in which the Brown-York charge is extended beyond the black hole horizon. This extension naturally generalizes the scattering problem to configurations that foliate the black hole interior.
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BibTeX
@misc{griguolo2026quantum,
title = {{Quantum JT Gravity in a box as a Pöschl-Teller Scattering Problem}},
author = {Luca Griguolo and Jacopo Papalini and Lorenzo Russo and Domenico Seminara and Alex Tarana},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2607.01385},
eprint = {2607.01385},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.01385},
}
RIS
TY - UNPB
TI - Quantum JT Gravity in a box as a Pöschl-Teller Scattering Problem
AU - Luca Griguolo
AU - Jacopo Papalini
AU - Lorenzo Russo
AU - Domenico Seminara
AU - Alex Tarana
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2607.01385
UR - https://arxiv.org/abs/2607.01385
AB - We present a canonical quantization of Jackiw--Teitelboim gravity with finite Dirichlet boundary conditions, using the geodesic length between the two boundaries and its conjugate momentum as reduced phase space variables. The dynamics is recast as the scattering problem of a nonrelativistic particle in a repulsive Pöschl-Teller potential, naturally embedded within a hyperbolic reduction of the sl(2,ℝ) Casimir. We obtain exact wavefunctions of the universe and the disk partition function, interpreted as a transition matrix element between states of vanishing bare length. In the asymptotic limit, the theory reduces to Liouville quantum mechanics and reproduces the standard Schwarzian spectral density. At finite cutoff, however, the spectral measure exhibits genuinely nonperturbative corrections, absent in existing TT̅ approaches. These contributions admit an interpretation in terms of pinched disk geometries and are responsible for a controlled violation of the Wheeler-DeWitt equation. We also obtain closed form expressions for thermal two-point functions in terms of Wilson functions and propose diagrammatic rules for time- and out-of-time-ordered four-point functions. We further address the issue of the branch cut singularity of the quasi-local energy and propose a UV completion of the model in which the Brown-York charge is extended beyond the black hole horizon. This extension naturally generalizes the scattering problem to configurations that foliate the black hole interior.
ER -