The massless integer superspin multiplets revisited

We propose a new off-shell formulation for the massless $\mathcal{N}=1$ supersymmetric multiplet of integer superspin $s$ in four dimensions, where $s =2,3,\dots$(the$s=1$ case corresponds to the gravitino multiplet). Its gauge freedom matches that of the superconformal superspin-$s$ multiplet described in arXiv:1701.00682. The gauge-invariant action involves two compensating multiplets in addition to the superconformal superspin-$s$ multiplet. Upon imposing a partial gauge fixing, this action reduces to the one describing the so-called longitudinal formulation for the massless superspin-$s$ multiplet. Our new model is shown to possess a dual realisation obtained by applying a superfield Legendre transformation. We present a non-conformal higher spin supercurrent multiplet associated with the new integer superspin theory. This fermionic supercurrent is shown to occur in the Fayet-Sohnius model for a massive $\mathcal{N}=2$ hypermultiplet. We also give a new off-shell realisation for the massless gravitino multiplet.