Abstract
We initiate a systematic study of the self-interactions of a massive spin-2 “graviton” consistent with up to mathcal{N} = 4 supersymmetry. Using a recently developed massive on-shell superspace formalism, we construct the most general set of cubic massive graviton amplitudes in a form with all supersymmetry and Lorentz invariance manifest. We find that for mathcal{N} ≥ 3 supersymmetry, the family of consistent interactions coincide with those of the ghost-free dRGT model. For mathcal{N} = 4 (maximal) supersymmetry there is a single consistent cubic interaction which coincides with the unique structure required for the absence of asymptotic superluminality. Additionally, we discuss the structure of interactions in the high-energy limit, connections to supersymmetric Galileons and the possibility of a supersymmetric massive double copy.
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