Structure of 𝒩 = 2 superfield higher-spin abelian cubic interactions

Abstract

A bstract In this article we study the structure of the 𝒩 = 2 abelian higher-spin cubic ( s 1 , s 2 , s 2 ) vertices and the corresponding 𝒩 = 2 higher-spin supercurrents, introduced in arXiv:2408.00668 . These interactions are possible only for s 1 ≥ 2 s 2 . Conserved supercurrents are constructed as descendants of the principal supercurrent , which is uniquely characterized by simple differential conditions and admits an explicit representation in terms of 𝒩 = 2 higher-spin super-Weyl tensors. We derive the analytic form of the abelian vertices and identify the corresponding analytic higher-spin 𝒩 = 2 supercurrents. We show that the vertex structure is fully determined by the analytic supercurrents $${J}_{\alpha \left(s-1\right)\dot{\alpha }\left(s-1\right)}^{++}$$ , $${J}_{\alpha \left(s-1\right)\dot{\alpha }\left(s-2\right)}^{+}$$ and $${\overline{J} }_{\alpha \left(s-2\right)\dot{\alpha }\left(s-1\right)}^{+}$$ . 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 𝒩 = 2 vector multiplet associated with the ( s, 1, 1 ) interaction. In the rigid limit, for odd s these transformations reduce to the 𝒩 = 2 superspace generalization of zilch-type higher-spin symmetries.