From ChernTenenblat to JackiwTeitelboim via sineGordon
Abstract
The study of 2dimensional surfaces of constant curvature constitutes a beautiful branch of geometry with welldocumented ties to the mathematical physics of integrable systems. A lesser known, but equally fascinating, fact is its connection to 2dimensional gravity; specifically JackiwTeitelboim (JT) gravity, where the connection manifests through a coordinate choice that roughly speaking recasts the gravitational field equations as the sineGordon equation. In this language many wellknown results, such as the JTgravity black hole and its properties, were understood in terms of sineGordon solitons and their properties. In this brief note, we revisit these ideas in the context of some of the recent exciting developments in JTgravity and, more generally, lowdimensional quantum gravity and speculate on how some of these new ideas may be similarly understood.
 Publication:

arXiv eprints
 Pub Date:
 December 2021
 arXiv:
 arXiv:2201.00026
 Bibcode:
 2022arXiv220100026M
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Mathematical Physics
 EPrint:
 5+1 pages, 2 figures and lots of puns.This is a writeup of a lecture given at the Nankai Symposium on Mathematical Dialogues