Liouville theory beyond the cosmological horizon

TL;DR

This paper explores dualities between Euclidean Liouville theory and Einstein gravity in de Sitter space, revealing new insights into the spacetime interpretation of Liouville time and extending asymptotic symmetries.

Contribution

It demonstrates that Euclidean Liouville theory is dual to Einstein gravity with Dirichlet boundary conditions in the static patch of de Sitter space, extending the asymptotic symmetry algebra.

Findings

Euclidean Liouville theory is dual to Einstein gravity in the static patch.

Liouville time corresponds to the physical time of a static observer.

Asymptotic Virasoro algebra extends into the bulk.

Abstract

The dS/CFT correspondence postulates the existence of a Euclidean CFT dual to a suitable gravity theory with Dirichlet boundary conditions asymptotic to de Sitter spacetime. A semi-classical model of such a correspondence consists of Einstein gravity with positive cosmological constant and without matter which is dual to Euclidean Liouville theory defined at the future conformal boundary. Here we show that Euclidean Liouville theory is also dual to Einstein gravity with Dirichlet boundary conditions on a fixed timelike slice in the static patch. Intriguingly, the spacetime interpretation of Euclidean Liouville time is the physical time of the static observer. As a prerequisite of this correspondence, we show that the asymptotic symmetry algebra which consists of two copies of the Virasoro algebra extends everywhere into the bulk.