N = 2 superconformal higher-spin multiplets and their hypermultiplet couplings

We construct an off-shell N=2 superconformal cubic vertex for the hypermultiplet coupled to an arbitrary integer higher spin s gauge N=2 supermultiplet % in flatfour-dimensional space. in a general N=2 conformal supergravity background. We heavily use N=2, 4D harmonic superspace that provides an unconstrained superfield Lagrangian description. We start with 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 N=2, 4D 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 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.