Phase space of Jackiw-Teitelboim gravity with positive cosmological constant

TL;DR

This paper constructs and analyzes the classical phase space of Jackiw-Teitelboim gravity with positive cosmological constant, revealing its complex structure and potential for quantization.

Contribution

It provides the first detailed description of the phase space for this gravity model with positive cosmological constant, highlighting its singularities and group-theoretic structure.

Findings

Phase space has many singular points.

It is not Hausdorff.

Admits a group-theoretic description suitable for quantization.

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.