Higher-Spin dS/CFT beyond minimal type-A, and the doubled nature of de Sitter space

Abstract

We study the holographic duality between free vector models and Higher-Spin Gravity in 4-dimensional de Sitter space. On both the bulk and boundary sides, we introduce new reality conditions, which allow us to include odd spins in the bulk, and to extend the duality from type-A to type-B (i.e. from boundary scalars to spinors). The new reality conditions are closely related to a higher-spin-symmetric Hilbert-space norm for the single-particle (super)multiplet in de Sitter space. We construct two alternative viewpoints on the type-A and type-B theories. In one view, the two co-exist in "parallel universes", specifically in even vs. odd antipodal identifications of de Sitter space. In the other view, type-A and type-B are Legendre-transformed descriptions of the same twistor-space theory in Euclidean AdS (this involves the observation that the higher-spin partition function is Legendre-dual to itself). In this way, higher-spin holography reconciles the two-boundary nature of de Sitter space with the one-boundary nature of Euclidean AdS. The supersymmetric theory that unifies type-A and type-B with bulk fermions fails to be consistent under the appropriate reality conditions.