On higher-spin N = 2 supercurrent multiplets

We elaborate on the structure of higher-spin N = 2 supercurrent multiplets in four dimensions. It is shown that associated with every conformal supercurrent J_{α(m)α⋅(n)} (with m, n non-negative integers) is a descendant Jα(m+1)α⋅(n+1)ij with the following properties: (a) it is a linear multiplet with respect to its SU(2) indices, that is Dβ(iJα(m+1)α⋅(n+1)jk)=0 and D¯β̇(iJα(m+1)α⋅(n+1)jk)=0 ; and (b) it is conserved, ∂ββ⋅Jβα(m)β⋅α⋅(n)ij=0 . Realisations of the conformal supercurrents J_{α(s)α⋅(s)} , with s = 0, 1, …, are naturally provided by a massless hypermultiplet and a vector multiplet. It turns out that such supercurrents and their linear descendants Jα(s+1)α⋅(s+1)ij do not occur in the harmonic-superspace framework recently described by Buchbinder, Ivanov and Zaigraev. Making use of a massive hypermultiplet, we derive non-conformal higher-spin N = 2 supercurrent multiplets. Additionally, we derive the higher symmetries of the kinetic operators for both a massive and massless hypermultiplet. Building on this analysis, we sketch the construction of higher-derivative gauge transformations for the off-shell arctic multiplet Υ⁽¹⁾, which are expected to be vital in the framework of consistent interactions between Υ⁽¹⁾ and superconformal higher-spin gauge multiplets.