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

Jeff Murugan

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arXiv · 2201.00026

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

Jeff Murugan

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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.

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Jeff Murugan. 2021-12-31. From Chern-Tenenblat to Jackiw-Teitelboim via sine-Gordon. https://arxiv.org/abs/2201.00026

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