Non-Perturbative JT Gravity

TL;DR

This work addresses the non-perturbative instability of the Saad–Shenker–Stanford JT gravity formulation by constructing a non-perturbatively well-defined completion based on double-scaled complex matrix models. The approach preserves the high-energy perturbative JT physics, reproducing the Schwarzian spectral density, while introducing a stable low-energy sector governed by a string-equation framework and an auxiliary potential $u(x)$; a deformation parameter $μ$ tunes the low-energy behavior and connects to super JT gravity, with a further parameter $Γ$ accounting for RR-like fluxes. The analysis centers on Airy and Bessel prototype cases and a unique interpolating potential that avoids tunneling into $E<0$, supported by a universal differential equation for the spectral density derived from Gel'fand–Dikii relations, and a Miura-transformation-based treatment of $E=0$ via Painlevé II. The results yield a concrete, non-perturbatively stable JT gravity model that matches perturbative JT at high energy and smoothly connects to super JT gravity regimes, offering a robust platform for exploring holography, black-hole dynamics, and SYK-like physics within a controlled matrix-model framework.

Abstract

Recently, Saad, Shenker and Stanford showed how to define the genus expansion of Jackiw-Teitelboim quantum gravity in terms of a double-scaled Hermitian matrix model. However, the model's non-perturbative sector has fatal instabilities at low energy that they cured by procedures that render the physics non-unique. This might not be a desirable property for a system that is supposed to capture key features of quantum black holes. Presented here is a model with identical perturbative physics at high energy that instead has a stable and unambiguous non-perturbative completion of the physics at low energy. An explicit examination of the full spectral density function shows how this is achieved. The new model, which is based on complex matrix models, also allows for the straightforward inclusion of spacetime features analogous to Ramond-Ramond fluxes. Intriguingly, there is a deformation parameter that connects this non-perturbative formulation of JT gravity to one which, at low energy, has features of a super JT gravity.

Figures (10)

• Figure 1: The spectral density $\rho(E)$, both exactly (solid line) and numerically (crosses). The perturbative asymptote $\rho_{_0}\!(E){=}(\pi\hbar)^{-1}\sqrt{E}$ is shown as a dashed line for comparison.
• Figure 2: The spectral density $\rho(E)$ for the Bessel case, with $\Gamma{=}0$ and ${\tilde{\mu}}=\sqrt2$.
• Figure 3: A potential $u(x)$ that interpolates between the Airy case and the Bessel case. It is the unique $(k{=}1)$ solution to a special equation (\ref{['eq:string-equation-2']}) derived from a matrix model.
• Figure 4: The spectral density $\rho(E)$ extracted numerically (crosses) for the potential of figure \ref{['fig:potential']}, which is a solution of equation (\ref{['eq:string-equation-2']}). For comparison the exact Airy result is included (solid line). They differ significantly at low energies, with the new density terminating at a finite value at $E{=}0$. The perturbative asymptote $\rho_{_0}\!(E){=}(\pi\hbar)^{-1}\sqrt{E}$ is shown as a dashed line.
• Figure 5: The spectral density $\rho(E)$ extracted numerically (crosses) for the potential of figure \ref{['fig:potential']}, which is a solution of equation (\ref{['eq:string-equation-2']}). For comparison the exact Airy result is included (solid line). Parameter $\mu\,{=}\,{-}2$ has been turned on, pushing the distribution to the right.