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

Abstract

We construct an off-shell $\mathcal{N}=2$ superconformal cubic vertex for the hypermultiplet coupled to an arbitrary integer higher spin $\mathbf{s}$ 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 $\mathbf{s}$. 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 $\mathbf{s}$ multiplets in the Wess-Zumino gauges. The spin $\mathbf{s}$ multiplet involves $8(2\mathbf{s}-1{)}_B+8(2\mathbf{s}-1{)}_F$ 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.

0 + 60 pages, many corrections without affecting the final results; published version

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• $\mathcal{N}=2$ superconformal gravitino in harmonic superspace
• Unfolded hypermultiplet in harmonic superspace
• Supersymmetry at BLTP: Recent Progress in Two Directions
• Novel $\mathcal{N}=2$ higher-spin supercurrents