Unconstrained off-shell superfield formulation of $4D,\mathcal{N}=2$ supersymmetric higher spins

Abstract

We present, for the first time, the complete off-shell $4D,\mathcal{N}=2$ superfield actions for any free massless integer spin $\mathbf{s}\ge 2$ fields, using the $\mathcal{N}=2$ harmonic superspace approach. The relevant gauge supermultiplet is accommodated by two real analytic bosonic superfields $h_{\alpha (s-1)\dot{\alpha }(s-1)}^{++}$, $h_{\alpha (s-2)\dot{\alpha }(s-2)}^{++}$ and two conjugated complex analytic spinor superfields $h_{\alpha (s-1)\dot{\alpha }(s-2)}^{+3}$, $h_{\alpha (s-2)\dot{\alpha }(s-1)}^{+3}$, where $\alpha (s):=({\alpha }_1\dots {\alpha }_s),\dot{\alpha }(s):=({\dot{\alpha }}_1\dots {\dot{\alpha }}_s)$. Like in the harmonic superspace formulations of $\mathcal{N}=2$ Maxwell and supergravity theories, an infinite number of original off-shell degrees of freedom is reduced to the finite set (in WZ-type gauge) due to an infinite number of the component gauge parameters in the analytic superfield parameters. On shell, the standard spin content $(\mathbf{s},\mathbf{s}-1/2,\mathbf{s}-1/2,\mathbf{s}-1)$ is restored. For $\mathbf{s}=2$ the action describes the linearized version of "minimal" $\mathcal{N}=2$ Einstein supergravity.

0 + 29 pages, section 1 partly rearranged, section 4 extended, further typos corrected; published version

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• Off-shell invariants of linearized $4D,\mathcal{N}=2$ supergravity in the harmonic approach
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• Superspace First-order Formalism for Massless Arbitrary Superspin Supermultiplets
• Novel $\mathcal{N}=2$ higher-spin supercurrents
• Supersymmetry at BLTP: Recent Progress in Two Directions