On higher-spin ${\mathcal{N}=2}$ supercurrent multiplets

Abstract

We elaborate on the structure of higher-spin $\mathcal{N}=2$ supercurrent multiplets in four dimensions. It is shown that associated with every conformal supercurrent $J_{\alpha(m) \dot{\alpha}(n)}$ (with $m,n$ non-negative integers) is a descendant $J^{ij}_{\alpha(m+1) \dot{\alpha}(n+1)}$ with the following properties: (a) it is a linear multiplet with respect to its $\mathsf{SU}(2)$ indices, that is $ D_\beta^{(i} J^{ jk)}_{\alpha(m+1) \dot{\alpha}(n+1) }=0$ and $ \bar D_{\dot \beta}^{(i} J^{jk)}_{ \alpha(m+1) \dot{\alpha}(n+1) }=0$; and (b) it is conserved, $\partial^{\beta \dot{\beta}} J^{ij}_{\beta \alpha(m) \dot{\beta} \dot{\alpha}(n)}=0$. Realisations of the conformal supercurrents $J_{\alpha(s) \dot{\alpha}(s)}$, with $s=0,1, \dots$, are naturally provided by a massless hypermultiplet and a vector multiplet. It turns out that such supercurrents and their linear descendants $J^{ij}_{\alpha(s+1) \dot{\alpha}(s+1)}$ do not occur in the harmonic-superspace framework recently described in arXiv:2212.14114. Making use of a massive hypermultiplet, we derive non-conformal higher-spin $\mathcal{N}=2$ 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 $\Upsilon^{(1)}$, which are expected to be vital in the framework of consistent interactions between $\Upsilon^{(1)}$ and superconformal higher-spin gauge multiplets.