Conserved higher spin supercurrents for arbitrary spin massless supermultiplets and higher spin superfield cubic interactions

Abstract

We give an explicit superspace construction of higher spin conserved supercurrents built out of 4D, mathcal{N}=1 massless supermultiplets of arbitrary spin. These supercurrents are gauge invariant and generate a large class of cubic interactions between a massless supermultiplet with superspin Y1 = s1 + 1/2 and two massless supermultiplets of arbitrary superspin Y2. These interactions are possible only for s1 ≥ 2Y2. At the equality, the supercurrent acquires its simplest form and defines the supersymmetric, higher spin extension of the linearized Bel-Robinson tensor.