The Asymptotic Dynamics of de Sitter Gravity in three Dimensions

TL;DR

The paper addresses the holographic description of 3D gravity with positive cosmological constant by recasting the theory as a $SL(2,C)$ Chern-Simons theory and deriving the asymptotic boundary dynamics. It demonstrates, via a two-step reduction, that the boundary theory is Euclidean Liouville theory on the past boundary ${ m I}^-$, providing an explicit dS/CFT realization. The approach clarifies how the bulk de Sitter asymptotic Virasoro structure emerges from boundary conformal dynamics through a sequence of WZNW reductions and gauging. This work offers a concrete, computable instance of de Sitter holography and informs potential future explorations of holonomies and single-boundary duals.

Abstract

We show that the asymptotic dynamics of three-dimensional gravity with positive cosmological constant is described by Euclidean Liouville theory. This provides an explicit example of a correspondence between de Sitter gravity and conformal field theories. In the case at hand, this correspondence is established by formulating Einstein gravity with positive cosmological constant in three dimensions as an SL(2,C) Chern-Simons theory. The de Sitter boundary conditions on the connection are divided into two parts. The first part reduces the CS action to a nonchiral SL(2,C) WZNW model, whereas the second provides the constraints for a further reduction to Liouville theory, which lives on the past boundary of dS_3.