( \mathcal{N} \) = 2 supersymmetric partially massless fields and other exotic non-unitary superconformal representations

We find and classify the simplest \( \mathcal{N} \) = 2 SUSY multiplets on AdS4 which contain partially massless fields. We do this by studying representations of the \( \mathcal{N} \) = 2, d = 3 superconformal algebra of the boundary, including new shortening conditions that arise in the non-unitary regime. Unlike the \( \mathcal{N} \) = 1 case, the simplest \( \mathcal{N} \) = 2 multiplet containing a partially massless spin-2 is short, containing several exotic fields. More generally, we argue that \( \mathcal{N} \) = 2 supersymmetry allows for short multiplets that contain partially massless spin-s particles of depth t = s – 2.