Solitons and Black Holes

TL;DR

This paper investigates the deep connection between black holes in JT dilaton gravity and sine-Gordon solitons, revealing new insights into their mathematical structure and symmetries, and constructing a gauge theory formulation from soliton transformations.

Contribution

It demonstrates that solutions to JT dilaton gravity equations correspond to sine-Gordon solitons and constructs a gauge theory framework using Bäcklund transformations.

Findings

Dilaton solutions solve the sine-Gordon equation linearized around solitons.

Dilaton fields relate to symmetries of soliton solutions.

A flat SL(2,R) connection is constructed from Bäcklund transformations.

Abstract

We explore the relationship between black holes in Jackiw-Teitelboim(JT) dilaton gravity and solitons in sine-Gordon field theory. Our analysis expands on the well known connection between solutions of the sine-Gordon equation and constant curvature metrics. In particular, we show that solutions to the dilaton field equations for a given metric in JT theory also solve the sine-Gordon equation linearized about the corresponding soliton. Since the dilaton generates Killing vectors of the constant curvature metric, it is interesting that it has an analoguous interpretation in terms of symmetries of the soliton solution. We also show that from the B${\ddot a}$cklund transformations relating different soliton solutions, it is possible to construct a flat SL(2,R) connection which forms the basis for the gauge theory formulation of JT dilaton gravity.