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 $J_{\alpha (m+1)\dot{\alpha }(n+1)}^{ij}$ with the following properties: (a) it is a linear multiplet with respect to its $\mathsf{SU}(2)$ indices, that is $D_{\beta }^{(i}{J}_{\alpha (m+1)\dot{\alpha }(n+1)}^{jk)}=0$ and ${\bar{D}}_{\dot{\beta }}^{(i}{J}_{\alpha (m+1)\dot{\alpha }(n+1)}^{jk)}=0$; and (b) it is conserved, ${\partial }^{\beta \dot{\beta }}{J}_{\beta \alpha (m)\dot{\beta }\dot{\alpha }(n)}^{ij}=0$. 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 $J_{\alpha (s+1)\dot{\alpha }(s+1)}^{ij}$ 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 ${{\rm Y}}^{(1)}$, which are expected to be vital in the framework of consistent interactions between ${{\rm Y}}^{(1)}$ and superconformal higher-spin gauge multiplets.

23 pages; V2: comments, references and a new appendix added; V3: published version

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Cited by in corpus (3)

• $\mathcal{N}=2$ superconformal higher-spin multiplets and their hypermultiplet couplings
• Three-point functions of conserved currents in 4D CFT: general formalism for arbitrary spins
• Novel $\mathcal{N}=2$ higher-spin supercurrents