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

A bstract We study cubic interactions of $$ \mathcal{N} $$ N = 2 massless integer-spin gauge supermultiplets in harmonic superspace. We construct the complete class of abelian ( s , s 1 , s 2 ) cubic vertices with the minimal number of space-time derivatives. Such vertices exist only for s ≥ s 1 + s 2 and universally take the form of the gauge prepotential coupled to the conserved higher-spin supercurrent. For s 1 ≠ 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 $$ \mathcal{N} $$ N = 2 higher-spin Weyl supertensors associated with the spin- s 1 and spin- 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.