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A bstract Given a maximally symmetric d -dimensional background with isometry algebra g g, a symmetric and traceless rank- s field ϕ a (s) satisfying the massive Klein-Gordon equation furnishes a collection of massive g g -representations with spins j ∈ 0, 1, · · ·, s. In this paper we construct the spin- (s, j) projectors, which are operators that isolate the part of ϕ a (s) that furnishes the representation from this collection carrying spin j. In the case of an (anti-) de Sitter ( (A) dS d) background, we find that the poles of the projectors encode information about (partially-) massless representations, in agreement with observations made earlier in d = 3, 4. We then use these projectors to facilitate a systematic derivation of two-derivative actions with a propagating massless spin- s mode. In addition to reproducing the massless spin- s Fronsdal action, this analysis generates new actions possessing higher-depth gauge symmetry. In (A) dS d we also derive the action for a partially-massless spin- s depth- t field with 1 ≤ t ≤ s. The latter utilises the minimum number of auxiliary fields, and corresponds to the action originally proposed by Zinoviev after gauging away all Stückelberg fields. Some higher-derivative actions are also presented, and in d = 3 are used to construct (i) generalised higher-spin Cotton tensors in (A) dS 3 ; and (ii) topologically-massive actions with higher-depth gauge symmetry. Finally, in four-dimensional N N = 1 Minkowski superspace, we provide closed-form expressions for the analogous superprojectors.
Hutchings et al. (Wed,) studied this question.