$\mathcal{N} = 2$ superconformal higher-spin multiplets and their hypermultiplet couplings

TL;DR

This paper constructs off-shell $ ext{N}=2$ superconformal cubic vertices for hypermultiplets coupled to arbitrary higher spin gauge supermultiplets in flat space, using harmonic superspace techniques.

Contribution

It introduces a new off-shell superconformal coupling framework for hypermultiplets and higher spin multiplets in $ ext{N}=2$ supersymmetry using harmonic superspace.

Findings

Derived unconstrained analytic superconformal gauge potentials for arbitrary spin.

Established gauge transformation laws and off-shell content of higher-spin multiplets.

Explicitly constructed supercurrents for the cubic vertices.

Abstract

We construct an off-shell $\mathcal{N}=2$ superconformal cubic vertex for the hypermultiplet coupled to an arbitrary integer higher spin ${\bf s}$ gauge $\mathcal{N}=2$ supermultiplet % in flatfour-dimensional space. in a general $\mathcal{N}=2$ conformal supergravity background. We heavily use $\mathcal{N}=2, 4D$ harmonic superspace that provides an unconstrained superfield Lagrangian description. We start with $\mathcal{N}=2$ global superconformal symmetry transformations of the free hypermultiplet model and require invariance of the cubic vertices of general form under these transformations and their gauged version. As a result, we deduce $\mathcal{N}=2, 4D$ unconstrained analytic superconformal gauge potentials for an arbitrary integer ${\bf s}$. These are the basic ingredients of the approach under consideration. We describe the properties of the gauge potentials, derive the corresponding superconformal and gauge transformation laws, and inspect the off-shell contents of the thus obtained $\mathcal{N}=2$ superconformal higher-spin ${\bf s}$ multiplets in the Wess-Zumino gauges. The spin ${\bf s}$ multiplet involves $8(2{\bf s} -1)_B + 8(2{\bf s}-1)_F$ essential off-shell degrees of freedom. The cubic vertex has the generic structure higher spin gauge superfields $\times$ hypermultiplet supercurrents. We present the explicit form of the relevant supercurrents.