Probing de Sitter Space Using CFT States

TL;DR

This paper constructs and analyzes CFT states dual to local excitations in de Sitter space, revealing unique conjugation properties and explaining the emergence of time from the Euclidean CFT, with implications for holography.

Contribution

It introduces a novel construction of bulk local states in dS/CFT, highlighting differences from AdS/CFT and explaining the emergence of time in de Sitter holography.

Findings

Conjugation in dS/CFT differs from AdS/CFT.

Green's functions in dS Euclidean vacuum are not simple Wick rotations.

Information metric reproduces de Sitter space metric.

Abstract

In this paper we construct CFT states describing a putative holographic dual to local excitations in the three-dimensional de Sitter space (dS), called the bulk local states. We find that the conjugation operation in dS$_3/$CFT$_2$ is notably different from that in AdS$_3/$CFT$_2$. This requires us to combine two bulk local states constructed out of different primary states in a CPT-invariant way. This analysis explains why Green's functions in the dS Euclidean vacuum cannot simply be obtained from the Wick rotation of those in AdS. We also argue that this characteristic feature explains the emergence of a time coordinate from the dual Euclidean CFT. We show that the information metric for the quantum estimation of bulk coordinate values replicates the de Sitter space metric.