Explorations of Non-Perturbative JT Gravity and Supergravity

Abstract

Some recently proposed definitions of Jackiw-Teitelboim gravity and supergravities in terms of combinations of minimal string models are explored, with a focus on physics beyond the perturbative expansion in spacetime topology. While this formally involves solving infinite order non-linear differential equations, it is shown that the physics can be extracted to arbitrarily high accuracy in a simple controlled truncation scheme, using a combination of analytical and numerical methods. The non-perturbative spectral densities are explicitly computed and exhibited. The full spectral form factors, involving crucial non-perturbative contributions from wormhole geometries, are also computed and displayed, showing the non-perturbative details of the characteristic `slope', `dip', `ramp' and `plateau' features. It is emphasized that results of this kind can most likely be readily extracted for other types of JT gravity using the same methods.

Figures (33)

• Figure 1: The full spectral form factor, showing the classic (saxophone) shape made up of a slope, dip, ramp, and plateau. This is computed using the methods of this paper for the (2,2) model of JT supergravity. Here, $\beta{=}35$, $\hbar{=}1/5$. (See text.)
• Figure 2: The full spectral density, computed using the methods of this paper, for the (2,2) model of JT supergravity. The dashed blue line is the disc level result of equation (\ref{['eq:spectral_SJT']}). Here $\hbar{=}1$.
• Figure 3: The "nearly AdS$_2$" geometry, presented in two equivalent ways.
• Figure 4: Black holes vs. wormholes.
• Figure 5: The complete classical potential for JT supergravity (solid line). The uppermost dotted line is a truncation up to $t_2$, the lower dotted is a truncation up to $t_4$.