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 $J_{α(m) \dotα(n)}$ (with $m,n$ non-negative integers) is a descendant $J^{ij}_{α(m+1) \dotα(n+1)}$ with the following properties: (a) it is a linear multiplet with respect to its $\mathsf{SU}(2)$ indices, that is $ D_β^{(i} J^{ jk)}_{α(m+1) \dotα(n+1) }=0$ and $ \bar D_{\dot β}^{(i} J^{jk)}_{ α(m+1) \dotα(n+1) }=0$; and (b) it is conserved, $\partial^{β\dotβ} J^{ij}_{βα(m) \dotβ \dotα(n)}=0$. Realisations of the conformal supercurrents $J_{α(s) \dotα(s)}$, 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 $J^{ij}_{α(s+1) \dotα(s+1)}$ 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 $Υ^{(1)}$, which are expected to be vital in the framework of consistent interactions between $Υ^{(1)}$ and superconformal higher-spin gauge multiplets.