Structure of $\mathcal{N}=2$ superfield higher-spin abelian cubic interactions

In this article we study the structure of the $\mathcal{N}=2$ abelian higher-spin cubic $({\mathbf{s}}_{\mathbf{1}},{\mathbf{s}}_{\mathbf{2}},{\mathbf{s}}_{\mathbf{2}})$ vertices and the corresponding $\mathcal{N}=2$ higher-spin supercurrents, introduced in arXiv:2408.00668. These interactions are possible only for ${\mathbf{s}}_{\mathbf{1}}\ge 2{\mathbf{s}}_{\mathbf{2}}$. Conserved supercurrents are constructed as descendants of the $\mathit{\text{principal}}\mathit{\text{supercurrent}}$, which is uniquely characterized by simple differential conditions and admits an explicit representation in terms of $\mathcal{N}=2$ higher-spin super-Weyl tensors. We derive the analytic form of the abelian vertices and identify the corresponding analytic higher-spin $\mathcal{N}=2$ supercurrents. We show that the vertex structure is fully determined by the analytic supercurrents $J_{\alpha (s-1)\dot{\alpha }(s-1)}^{++}$, $J_{\alpha (s-1)\dot{\alpha }(s-2)}^{+}$, and ${\bar{J}}_{\alpha (s-2)\dot{\alpha }(s-1)}^{+}$. The analytic form of the vertices provides a simple framework for analyzing their component structure. As an example, we explore the component content of such interactions on the Bel–Robinson diagonal. Using the superfield inverse Noether procedure, we study higher-spin gauge transformations for the $\mathcal{N}=2$ vector multiplet associated with the $(\mathbf{s},\mathbf{1},\mathbf{1})$ interaction. In the rigid limit, for odd $\mathbf{s}$ these transformations reduce to the $\mathcal{N}=2$ superspace generalization of zilch-type higher-spin symmetries.