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 $\mathbf{ s_1}\geq 2 \mathbf{ s_2}$. 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.
Categories: hep-th