Confining Random Potential Quantum Mechanics for Jackiw-Teitelboim Gravity
Abstract
We formulate perturbative Jackiw-Teitelboim gravity as an ensemble of ordinary one-dimensional Hamiltonians with a confining random potential. The leading profile reproduces the disk density of states, while connected cumulants of a single master field encode the topological expansion. After formulating the cumulant power counting required by the topological expansion, we show that the cumulants reproduce all genus-zero multi-boundary amplitudes 𝒵0,n. At higher genus, we show that a renormalization scheme can be chosen consistently order by order so that imposing one-boundary polynomiality recursively reproduces the perturbative JT string equation and yields the standard JT one-boundary amplitudes 𝒵g,1. The framework provides a self-contained finite-S0 quantum dynamics with a discrete spectrum and unitary real time evolution, beyond a mere rewriting of the matrix integral. The same confining dynamics also underlies late-time saturation and the dynamical avoidance of the would-be black hole singularity, as shown in our earlier work.
Related
- Holonomies and boundary symmetries in discrete Jackiw–Teitelboim gravity
- Equations of state of hydrodynamic type and particle statistics of a Dyson gas in an analytic confining potential
- In light of the Henneaux-Teitelboim action
- Diffusive Description of Superconducting Single-Photon Detectors Using Quantum Mechanics
- The Klein-Gordon-Fock theory as a one-particle relativistic quantum mechanics
BibTeX
@misc{bak2026confining,
title = {{Confining Random Potential Quantum Mechanics for Jackiw-Teitelboim Gravity}},
author = {Dongsu Bak and Chanju Kim and Sang-Heon Yi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13286},
eprint = {2610.13286},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13286},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Confining Random Potential Quantum Mechanics for Jackiw-Teitelboim Gravity
AU - Dongsu Bak
AU - Chanju Kim
AU - Sang-Heon Yi
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13286
UR - https://arxiv.org/abs/2610.13286
AB - We formulate perturbative Jackiw-Teitelboim gravity as an ensemble of ordinary one-dimensional Hamiltonians with a confining random potential. The leading profile reproduces the disk density of states, while connected cumulants of a single master field encode the topological expansion. After formulating the cumulant power counting required by the topological expansion, we show that the cumulants reproduce all genus-zero multi-boundary amplitudes 𝒵_0,n. At higher genus, we show that a renormalization scheme can be chosen consistently order by order so that imposing one-boundary polynomiality recursively reproduces the perturbative JT string equation and yields the standard JT one-boundary amplitudes 𝒵_g,1. The framework provides a self-contained finite-S_0 quantum dynamics with a discrete spectrum and unitary real time evolution, beyond a mere rewriting of the matrix integral. The same confining dynamics also underlies late-time saturation and the dynamical avoidance of the would-be black hole singularity, as shown in our earlier work.
ER -