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

TL;DR

This paper investigates the structure and properties of higher-spin $ ext{N}=2$ supercurrent multiplets in four dimensions, revealing new linear and conserved descendants, and exploring their realizations and gauge transformations.

Contribution

It introduces a detailed structure of higher-spin $ ext{N}=2$ supercurrent multiplets, including their descendants and conservation properties, and constructs non-conformal multiplets using massive hypermultiplets.

Findings

Revealed the structure of descendant supercurrents with specific properties.

Provided realizations of supercurrents via hypermultiplets and vector multiplets.

Derived higher symmetries and gauge transformations for supermultiplets.

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.