Mixed-symmetry fields in de Sitter space: a group theoretical glance

Abstract

We rederive the characters of all unitary irreducible representations of the $(d+1)$-dimensional de Sitter spacetime isometry algebra $\mathfrak{so}(1,d+1)$, 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 comment on a possible equivalent of the scalar singleton for the de Sitter (dS) spacetime.

40 pages, 4 figures; v2: typos corrected, flat limit of the complementary series refined and references added; v3: typos corrected; v4: improved discussion on the role of the primary Weyl tensor + typos corrected in appendices

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• A theory for multiple partially massless spin-2 fields
• (Non-)unitarity of strictly and partially massless fermions on de Sitter space II: an explanation based on the group-theoretic properties of the spin-3/2 and spin-5/2 eigenmodes
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• New conformal-like symmetry of strictly massless fermions in four-dimensional de Sitter space
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• Character Integral Representation of Zeta function in AdS${}_{d+1}$: I. Derivation of the general formula
• Dynamical Edge Modes in $p$-form Gauge Theories
• Fermionic Shift Symmetries in (Anti) de Sitter Space
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• On the consistency of (partially-)massless matter couplings in de Sitter space
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• Hidden Conformal Symmetry of the Discrete Series Scalars in dS${}_2$
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• Real-time observables in de Sitter thermodynamics
• De Sitter Horizon Edge Partition Functions
• Partition functions of $p$-forms from Harish-Chandra characters
• Diagonalization Procedure for Reducible Massless N=1 Supermultiplets
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• De Sitter scattering amplitudes in the Born approximation
• Probing CP-violating Higgs-Gauge couplings with Higgsstrahlung at $e^{-}{e}^{+}$ collider