State/Operator Correspondence in Higher-Spin dS/CFT

TL;DR

This paper explores the holographic duality between higher-spin gravity in de Sitter space and a three-dimensional Euclidean $Sp(N)$ CFT, clarifying the correspondence of states and vacua in this dS/CFT framework.

Contribution

It provides a detailed holographic dictionary for dS/CFT relating boundary states to bulk states, including vacua and operator insertions, in the context of higher-spin gravity.

Findings

Boundary CFT states on $S^2$ correspond to bulk states on $R^3$ slices.

Ground states of the $Sp(N)$ model relate to dS-invariant vacua.

Operator insertions in CFT correspond to (anti) quasinormal modes in the bulk.

Abstract

A recently conjectured microscopic realization of the dS$_4$/CFT$_3$ correspondence relating Vasiliev's higher-spin gravity on dS$_4$ to a Euclidean $Sp(N)$ CFT$_3$ is used to illuminate some previously inaccessible aspects of the dS/CFT dictionary. In particular it is argued that states of the boundary CFT$_3$ on $S^2$ are holographically dual to bulk states on geodesically complete, spacelike $R^3$ slices which terminate on an $S^2$ at future infinity. The dictionary is described in detail for the case of free scalar excitations. The ground states of the free or critical $Sp(N)$ model are dual to dS-invariant plane-wave type vacua, while the bulk Euclidean vacuum is dual to a certain mixed state in the CFT$_3$. CFT$_3$ states created by operator insertions are found to be dual to (anti) quasinormal modes in the bulk. A norm is defined on the $R^3$ bulk Hilbert space and shown for the scalar case to be equivalent to both the Zamolodchikov and pseudounitary C-norm of the $Sp(N)$ CFT$_3$.