N=2 abelian higher-spin cubic (s1,s2,s2) vertices have analytic structure fully fixed by the supercurrents J++_{\alpha(s-1)\dot{\alpha}(s-1)}, J^+_{\alpha(s-1)\dot{\alpha}(s-2)} and \bar J^+_{\alpha(s-2)\dot{\alpha}(s-1)} for s1 \ge 2 s2.
Conserved higher spin supercurrents for arbitrary spin massless supermultiplets and higher spin superfield cubic interactions
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abstract
We give an explicit superspace construction of higher spin conserved supercurrents built out of $4D,\mathcal{N}=1$ massless supermultiplets of arbitrary spin. These supercurrents are gauge invariant and generate a large class of cubic interactions between a massless supermultiplet with superspin $Y_1=s_1+1/2$ and two massless supermultiplets of arbitrary superspin $Y_2$. These interactions are possible only for $s_1\geq 2Y_2$. At the equality, the supercurrent acquires its simplest form and defines the supersymmetric, higher spin extension of the linearized Bel-Robinson tensor.
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Structure of $\mathcal{N} = 2$ superfield higher-spin abelian cubic interactions
N=2 abelian higher-spin cubic (s1,s2,s2) vertices have analytic structure fully fixed by the supercurrents J++_{\alpha(s-1)\dot{\alpha}(s-1)}, J^+_{\alpha(s-1)\dot{\alpha}(s-2)} and \bar J^+_{\alpha(s-2)\dot{\alpha}(s-1)} for s1 \ge 2 s2.