$\mathcal{N}=2$ Supersymmetric Partially Massless Fields and Non-Unitary Superconformal Representations

Abstract

We find and classify the simplest $\mathcal{N}=2$ SUSY multiplets on AdS${}_4$ 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 $t=s-2$.

62 pages, 6 tables, 11 figures