The Asymptotic Dynamics of two-dimensional (anti-)de Sitter Gravity

TL;DR

This paper demonstrates that the long-term behavior of two-dimensional (anti-)de Sitter JT gravity can be modeled by a two-particle Calogero-Sutherland system, linking gravity to integrable quantum mechanics.

Contribution

It establishes a novel connection between 2D (A)dS gravity and Calogero-Sutherland models via a boundary gauge theory reduction.

Findings

JT gravity dynamics maps to Calogero-Sutherland model

Boundary reduction yields a nonlinear sigma model

Cyclic coordinates enable further reduction to quantum mechanics

Abstract

We show that the asymptotic dynamics of two-dimensional de Sitter or anti-de Sitter Jackiw-Teitelboim (JT) gravity is described by a generalized two-particle Calogero-Sutherland model. This correspondence is established by formulating the JT model of (A)dS gravity in two dimensions as a topological gauge theory, which reduces to a nonlinear 0+1-dimensional sigma model on the boundary of (A)dS space. The appearance of cyclic coordinates allows then a further reduction to the Calogero-Sutherland quantum mechanical model.