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

TL;DR

This work addresses the problem of characterizing the asymptotic dynamics of two-dimensional Jackiw-Teitelboim gravity with AdS or dS cosmological constant. It develops a top-down construction by reformulating JT gravity as a topological SU(1,1) gauge theory, reducing the boundary dynamics to a 0+1D nonlinear sigma model, and then applying cyclic-coordinate (Routhian) reduction to a generalized two-particle Calogero-Sutherland quantum mechanics; the construction is shown to extend to dS$_2$ with Euclidean boundary. The key contributions are the explicit boundary reduction to a sigma model, the subsequent reduction to an integrable Calogero-Sutherland type quantum mechanics, and the demonstration that the same mechanism works for both AdS$_2$ and dS$_2$. This work connects the asymptotic dynamics of 2D (A)dS gravity to an integrable quantum-mechanical model, generalizing known 3D results (e.g., Liouville theory from WZNW reduction) and suggesting future directions such as supersymmetric extensions and links to the CGHS model.

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.