On the reconstruction map in JT gravity

TL;DR

This paper constructs a physically-motivated reconstruction map in JT gravity, enabling precise quantum bulk operator analysis and revealing non-perturbative effects on wormhole dynamics, with implications for holographic complexity.

Contribution

It explicitly constructs a reconstruction map in JT gravity using action-angle variables, matching known spectral results and analyzing quantum wormhole dynamics.

Findings

Average wormhole length is non-monotonic in time.

Quantum fluctuations of wormhole length are suppressed until the Heisenberg time.

Late-time state exhibits a heavy-tailed distribution of lengths.

Abstract

An open question in AdS/CFT is how to reconstruct semiclassical bulk operators precisely enough that non-perturbative quantum effects can be computed. We propose a set of physically-motivated requirements for such a reconstruction map, and explicitly construct a map satisfying these requirements in Jackiw-Teitelboim (JT) gravity. Our map is found by canonically quantizing "action-angle" variables for JT gravity, which are chosen to ensure that the spectrum of the fundamental quantum theory matches known results from the gravitational path integral. We then study unitary quantum dynamics in this theory, and obtain analytical predictions for the dynamics of the wormhole length, including its quantum fluctuations, leveraging techniques from quantum ergodicity theory. Level repulsion in the non-perturbative JT spectrum implies that the average wormhole length is non-monotonic in time, that fluctuations in wormhole length are non-perturbatively suppressed until nearly the Heisenberg time, and that the late-time-evolved Hartle-Hawking state has a heavy-tailed distribution of lengths. We discuss the implications of our results for the "complexity = volume" conjecture.