From Two-dimensional Black Holes to sine-Gordon Solitons

Abstract

We show that there exists an intriguing connection between black holes in Jackiw-Teitelboim dilaton gravity and Euclidean sine-Gordon solitons. Our analysis exploits a well-known relationship between constant curvature metrics and sine-Gordon solitons to show that in a particular coordinate system, the Jackiw-Teitelboim action reduces precisely to the Euclidean sine-Gordon theory. We construct explicitly the coordinate transformation relating these “sine-Gordon coordinates” to the standard black hole coordinates and show how Backlund transformations of the soliton theory lead to the gauge theory formulation of Jackiw-Teitelboim gravity. We also speculate on the significance of these results for investigations of black hole entropy.