Abstract:We derive the characters of all unitary irreducible representations of the (d+1)-dimensional de Sitter spacetime isometry algebra so(1, d + 1), and propose a dictionary between those representations and massive or (partially) massless fields on de Sitter spacetime. We propose a way of taking the flat limit of representations in (anti-) de Sitter spaces in terms of these characters, and conjecture the spectrum resulting from taking the flat limit of mixed-symmetry fields in de Sitter spacetime. We identify the equivalent of the scalar singleton for the de Sitter (dS) spacetime.

We prove a generalized Flato-Fronsdal theorem for higher-order, scalar and spinor, singletons. In the resulting infinite tower of bulk higher-spin fields, we point out the occurrence of partially-massless fields of all depths. This leads us to conjecture a holographic duality between a higher-spin gravity theory around AdS d+1 with the aforementioned spectrum of fields, and a free CF T d of fundamental (higher-order) scalar and spinor singletons. As a first check of this conjecture, we find that the total Casimir energy vanishes at one loop.