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

Abstract

In this article we study the structure of the $\mathcal{N}=2$ abelian higher-spin cubic $({\mathbf{s}}_1,{\mathbf{s}}_2,{\mathbf{s}}_2)$ vertices and the corresponding $\mathcal{N}=2$ higher-spin supercurrents, introduced in arXiv:2408.00668. These interactions are possible only for ${\mathbf{s}}_1\ge 2{\mathbf{s}}_2$. Conserved supercurrents are constructed as descendants of the \textit{principal 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 $J_{\hat{I}\pm (s-1)\dot{\hat{I}}\pm (s-1)}^{++}$, $J_{\hat{I}\pm (s-1)\dot{\hat{I}}\pm (s-2)}^{+}$, and ${\bar{J}}_{\hat{I}\pm (s-2)\dot{\hat{I}}\pm (s-1)}^{+}$. 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 $(\mathbf{s},1,1)$ 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.

0 + 57 pages, matches version accepted for publication in JHEP