The Asymptotic Dynamics of de Sitter Gravity in three Dimensions

TL;DR

This paper demonstrates that the asymptotic behavior of three-dimensional de Sitter gravity can be described by Euclidean Liouville theory, establishing a link between de Sitter space and conformal field theories through Chern-Simons formulation.

Contribution

It explicitly formulates 3D de Sitter gravity as an SL(2,C) Chern-Simons theory and derives its boundary dynamics as Liouville theory, providing a concrete example of dS/CFT correspondence.

Findings

De Sitter gravity corresponds to Euclidean Liouville theory at the boundary.

Boundary conditions reduce the Chern-Simons action to Liouville theory.

The approach clarifies the holographic nature of de Sitter space in three dimensions.

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.