De Sitter Invariant Vacuum States, Vertex Operators, and Conformal Field Theory Correlators

TL;DR

This paper identifies a unique de Sitter invariant vacuum state for quantum fields, computes vertex operator correlations, and shows their limits reproduce conformal field theory correlators on the boundary.

Contribution

It establishes the uniqueness of the de Sitter invariant vacuum and links vertex operator correlations in de Sitter space to boundary conformal field theory correlators.

Findings

Unique de Sitter invariant vacuum state identified.

Correlation functions of vertex operators match boundary CFT correlators.

Correlation functions on Lobachevsky space also reproduce CFT correlators.

Abstract

We show that there is only one physically acceptable vacuum state for quantum fields in de Sitter space-time which is left invariant under the action of the de Sitter-Lorentz group $SO(1,d)$ and supply its physical interpretation in terms of the Poincare invariant quantum field theory (QFT) on one dimension higher Minkowski spacetime. We compute correlation functions of the generalized vertex operator $:e^{i\hat{S}(x)}:$, where $\hat{S}(x)$ is a massless scalar field, on the $d$-dimensional de Sitter space and demonstrate that their limiting values at timelike infinities on de Sitter space reproduce correlation functions in $(d-1)$-dimensional Euclidean conformal field theory (CFT) on $S^{d-1}$ for scalar operators with arbitrary real conformal dimensions. We also compute correlation functions for a vertex operator $e^{i\hat{S}(u)}$ on the \L obaczewski space and find that they also reproduce correlation functions of the same CFT. The massless field $\hat{S}(u)$ is the nonlocal transform of the massless field $\hat{S}(x)$ on de Sitter space introduced by one of us.