$\mathcal{N}=2$ higher-spin supercurrents

Abstract

We have constructed conserved $\mathcal{N}=2$ higher-spin supercurrents for an arbitrary integer spin through the unconstrained superfield formulation of $4D,\mathcal{N}=2$ massless higher-spin theories in the harmonic superspace. The obtained supercurrents are gauge-invariant and determine consistent cubic interactions in the \textit{gauge superfield} $\times$ \textit{supercurrent} form for massless spin ${\mathbf{s}}_1$ and two massless spin ${\mathbf{s}}_2$ $\mathcal{N}=2$ supermultiplets. Such interactions and $\mathcal{N}=2$ supercurrents exist only for ${\mathbf{s}}_1\ge 2{\mathbf{s}}_2$. These supercurrents are the $\mathcal{N}=2$ supersymmetric extension of Berends-Burgers-van Dam higher-spin currents and generalize the linearized Bel-Robinson tensor. The relevant $\mathcal{N}=2$ supercurrents can be considered as the descendants of the $\mathcal{N}=2$ principle supercurrent, which has a simple universal structure. An important feature of our outcomes is that, ultimately, all $\mathcal{N}=2$ supercurrents are built from the $\mathcal{N}=2$ superfield strengths, which are constructed from the unconstrained analytical higher-spin prepotentials.

0 + 10 pages, typos corrected; published version