Phase space of Jackiw-Teitelboim gravity with positive cosmological constant

Abstract

In this paper we construct the classical phase space of Jackiw-Teitelboim gravity with positive cosmological constant on spatial slices with circle topology. This turns out to be somewhat more intricate than in the case of negative cosmological constant; this phase space has many singular points and is not even Hausdorff. Nonetheless, it admits a group-theoretic description which is quite amenable to quantization.

29 pages plus appendices, 10 figures. v2: references added, typos corrected, more explanation of the symplectic form calculation