Jackiw-Teitelboim quantum gravity with defects and the Aharonov-Bohm effect

TL;DR

This paper explores Jackiw-Teitelboim gravity with defects, showing it can be mapped to a charged particle in a magnetic field with Aharonov-Bohm effects, enabling exact calculations of quantum gravitational properties and their impact on entropy and chaos.

Contribution

It introduces a novel mapping of JT gravity with defects to a quantum mechanics model, allowing exact solutions and analysis of entropy and correlation modifications due to defects.

Findings

Exact wavefunctions and propagators for the gravitational system

Reproduction of classical and topological entropy contributions

Modification of correlation functions and Lyapunov exponent due to defects

Abstract

We study the theory of Jackiw-Teitelboim gravity with generalized dilaton potential on Euclidean two-dimensional negatively curved backgrounds. The effect of the generalized dilaton potential is to induce a conical defect on the two-dimensional manifold. We show that this theory can be written as the ordinary quantum mechanics of a charged particle on a hyperbolic disk in the presence of a constant background magnetic field plus a pure gauge Aharonov-Bohm field. This picture allows us to exactly calculate the wavefunctions and propagators of the corresponding gravitational dynamics. With this method we are able to reproduce the gravitational density of states as well as compute the R\'eyni and entanglement entropies for the Hartle-Hawking state. While we reproduce the classical entropy at high temperature, we also find an extra topological contribution that becomes dominant at low temperatures. We then show how the presence of defects modify correlation functions, including the out-of-time-ordered correlation, and decrease the Lyapunov exponent. This is achieved two ways: by directly quantizing the boundary Schwarzian theory and by dimensionally reducing $SL(2,\mathbb{Z})$ black holes.