Progress on cubic interactions of arbitrary superspin supermultiplets via gauge invariant supercurrents

We consider cubic interactions of the form s - Y - Y between a massless integer superspin s supermultiplet and two massless arbitrary integers or half integer superspin Y supermultiplets. We focus on non-minimal interactions generated by gauge invariant supercurrent multiplets which are bilinear in the superfield strength of the superspin Y supermultiplet. We find two types of consistent supercurrents. The first one corresponds to conformal integer superspin s supermultiplets, exist only for even values of s, s = 2l + 2, for arbitrary values of Y and it is unique. The second one, corresponds to Poincare integer superspin s supermultiplets, exist for arbitrary values of sand Y. (C) 2019 The Authors. Published by Elsevier B.V.