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

We construct an off-shell $$ \mathcal{N} $$ N = 2 superconformal cubic vertex for the hypermultiplet coupled to an arbitrary integer higher spin s gauge $$ \mathcal{N} $$ N = 2 supermultiplet in a general $$ \mathcal{N} $$ N = 2 conformal supergravity background. We heavily use $$ \mathcal{N} $$ N = 2 , 4 D harmonic superspace that provides an unconstrained superfield Lagrangian description. We start with $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ N = 2 , 4 D unconstrained analytic superconformal gauge potentials for an arbitrary integer 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 $$ \mathcal{N} $$ N = 2 superconformal higher-spin s multiplets in the Wess-Zumino gauges. The spin s multiplet involves 8(2 s − 1) B + 8(2 s − 1) F essential off-shell degrees of freedom. The cubic vertex has the generic structure higher spin gauge superfields × hypermultiplet supercurrents . We present the explicit form of the relevant supercurrents.