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

TL;DR

This paper constructs explicit higher spin conserved supercurrents in 4D, N=1 superspace, enabling new cubic interactions among massless supermultiplets with arbitrary spins, extending known superfield structures.

Contribution

It provides the first explicit superspace construction of gauge-invariant higher spin supercurrents for arbitrary supermultiplet spins, facilitating new cubic interaction models.

Findings

Supercurrents are gauge invariant and generate cubic interactions.

Interactions occur only for specific spin relations, s_1 ≥ 2Y_2.

Supercurrent simplifies at the equality, extending the Bel-Robinson tensor.

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 $Y_1=s_1+1/2$ and two massless supermultiplets of arbitrary superspin $Y_2$. These interactions are possible only for $s_1\geq 2Y_2$. At the equality, the supercurrent acquires its simplest form and defines the supersymmetric, higher spin extension of the linearized Bel-Robinson tensor.