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 $\mathbf{s}\ge {\mathbf{s}}_1+{\mathbf{s}}_2$ and universally take the form of the gauge prepotential coupled to the conserved higher-spin supercurrent. For~${\mathbf{s}}_1\ne {\mathbf{s}}_2$, 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.

0+15 pages; In honor of the 70th anniversary of the Bogoliubov Laboratory of Theoretical Physics; to appear in JHEP