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

TL;DR

This paper constructs gauge-invariant $ ext{N}=2$ higher-spin supercurrents in 4D superspace, enabling consistent cubic interactions for massless supermultiplets, extending known higher-spin currents with a universal superfield structure.

Contribution

It introduces a method to construct $ ext{N}=2$ higher-spin supercurrents for arbitrary integer spins using harmonic superspace, generalizing previous higher-spin current formulations.

Findings

Supercurrents are gauge-invariant and determine cubic interactions.

Existence of supercurrents requires $s_1 ext{ } ext{ge} ext{ } 2 s_2$.

Supercurrents are built from superfield strengths derived from unconstrained prepotentials.

Abstract

We have constructed conserved $\mathcal{N}=2$ higher-spin supercurrents for an arbitrary integer spin through the unconstrained superfield formulation of $4D,\, \mathcal{N}=2$ massless higher-spin theories in the harmonic superspace. The obtained supercurrents are gauge-invariant and determine consistent cubic interactions in the \textit{gauge superfield} $\times$ \textit{supercurrent} form for massless spin $\mathbf{s_1}$ and two massless spin $\mathbf{s_2}$ $\mathcal{N}=2$ supermultiplets. Such interactions and $\mathcal{N}=2$ supercurrents exist only for $\mathbf{s_1}\geq 2 \mathbf{s_2}$. These supercurrents are the $\mathcal{N}=2$ supersymmetric extension of Berends-Burgers-van Dam higher-spin currents and generalize the linearized Bel-Robinson tensor. The relevant $\mathcal{N}=2$ supercurrents can be considered as the descendants of the $\mathcal{N}=2$ principle supercurrent, which has a simple universal structure. An important feature of our outcomes is that, ultimately, all $\mathcal{N}=2$ supercurrents are built from the $\mathcal{N}=2$ superfield strengths, which are constructed from the unconstrained analytical higher-spin prepotentials.