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(alpha(m)alpha(over dot)(n)) (with m, n non-negative integers) is a descendant J(alpha(m+1)alpha(over dot)(n+1))(ij) with the following properties: (a) it is a linear multiplet with respect to its SU(2) indices, that is D-beta(alpha(m+1)alpha(over dot)(n+1))(i Jjk) = 0 and (D) over bar (beta(over dot)) ((ijk)) (alpha(m+1)alpha(over dot)(n+1))= 0; and (b) it is conserved, partial derivative(beta alpha(m)beta(over dot)alpha(over dot)(n)) (beta(beta) over bar Jij) = 0. Realisations of the conformal supercurrents J(alpha(s)alpha(over dot)(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 J(alpha(s+1)alpha(over dot)(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 (sic)((1),) which are expected to be vital in the framework of consistent interactions between (sic)((1)) and superconformal higher-spin gauge multiplets.