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

Understand

We consider cubic interactions of the form $s-Y-Y$ between a massless integer superspin $s$ supermultiplet and two massless arbitrary integer 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 $s, s=2\ell+2$, for arbitrary values of $Y$ and it is unique.