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

Abstract

Abstract We elaborate on the structure of higher-spin $$ \mathcal{N} $$ N = 2 supercurrent multiplets in four dimensions. It is shown that associated with every conformal supercurrent $$ {J}_{\alpha (m)\overset{\cdot }{\alpha }(n)} $$ J α m α ⋅ n (with m, n non-negative integers) is a descendant $$ {J}_{\alpha \left(m+1\right)\overset{\cdot }{\alpha}\left(n+1\right)}^{ij} $$ J α 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 $$ {D}_{\beta}^{\Big(i}{J}_{\alpha \left(m+1\right)\overset{\cdot }{\alpha}\left(n+1\right)}^{jk\Big)}=0 $$ D β ( i J α m + 1 α ⋅ n + 1 jk ) = 0 and $$ {\overline{D}}_{\dot{\beta}}^{\Big(i}{J}_{\alpha \left(m+1\right)\overset{\cdot }{\alpha}\left(n+1\right)}^{jk\Big)}=0 $$ D ¯ β ̇ ( i J α m + 1 α ⋅ n + 1 jk ) = 0 ; and (b) it is conserved, $$ {\partial}^{\beta \overset{\cdot }{\beta }}{J}_{\beta \alpha (m)\overset{\cdot }{\beta}\overset{\cdot }{\alpha }(n)}^{ij}=0 $$ ∂ β β ⋅ J βα m β ⋅ α ⋅ n ij = 0 . Realisations of the conformal supercurrents $$ {J}_{\alpha (s)\overset{\cdot }{\alpha }(s)} $$ 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 $$ {J}_{\alpha \left(s+1\right)\overset{\cdot }{\alpha}\left(s+1\right)}^{ij} $$ J α 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 $$ \mathcal{N} $$ 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.