From Chern-Tenenblat to Jackiw-Teitelboim via sine-Gordon

TL;DR

This paper explores the deep connections between 2D geometry, integrable systems, and gravity, showing how sine-Gordon solitons relate to Jackiw-Teitelboim gravity and its recent developments.

Contribution

It revisits the link between sine-Gordon equations and JT gravity, providing insights into recent advances in low-dimensional quantum gravity.

Findings

JT black hole properties understood via sine-Gordon solitons

Recasting gravitational equations as integrable systems

Potential new interpretations of recent JT-gravity developments

Abstract

The study of 2-dimensional surfaces of constant curvature constitutes a beautiful branch of geometry with well-documented ties to the mathematical physics of integrable systems. A lesser known, but equally fascinating, fact is its connection to 2-dimensional gravity; specifically Jackiw-Teitelboim (JT) gravity, where the connection manifests through a coordinate choice that roughly speaking re-casts the gravitational field equations as the sine-Gordon equation. In this language many well-known results, such as the JT-gravity black hole and its properties, were understood in terms of sine-Gordon solitons and their properties. In this brief note, we revisit these ideas in the context of some of the recent exciting developments in JT-gravity and, more generally, low-dimensional quantum gravity and speculate on how some of these new ideas may be similarly understood.