Higher Spin Superfield interactions with Complex linear Supermultiplet: Conserved Supercurrents and Cubic Vertices

Understand

We continue the program of constructing cubic interactions between matter and higher spin supermultiplets.

• In this work we consider a complex linear superfield and we find that it can have cubic interactions only with supermultiplets with propagating spins $j=s+1$, $j=s+1/2$ for any non-negative integer $s$ (half-integer superspin supermultiplets).
• We construct the higher spin supercurrent and supertrace, these compose the canonical supercurrent multiplet which generates the cubic interactions.
• We also prove that for every $s$ there exist an alternative minimal supercurrent multiplet, with vanishing supertrace.