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

Abstract

We study cubic interactions of $\mathcal N=2$ massless integer-spin gauge supermultiplets in harmonic superspace. We construct the complete class of abelian $(\mathbf{s},\mathbf{s_1},\mathbf{s_2})$ cubic vertices with the minimal number of space-time derivatives. Such vertices exist only for $\mathbf{s}\geq \mathbf{s_1}+\mathbf{s_2}$ and universally take the form of the gauge prepotential coupled to the conserved higher-spin supercurrent. For~$\mathbf{s_1}\neq\mathbf{s_2}$, we find the novel complex principal supercurrent, whose real and imaginary parts generate the parity-invariant and the parity-breaking interactions, respectively. The supercurrents are constructed from gauge-invariant $\mathcal N=2$ higher-spin Weyl supertensors associated with the spin-$\mathbf{s_1}$ and spin-$\mathbf{s_2}$ gauge multiplets. These supertensors are defined in terms of unconstrained higher-spin analytic prepotentials. We also derive the complete set of conserved component higher-spin currents associated with the $(s,s_1,s_2)$ vertices, including both traceless currents and currents with the non-vanishing trace.