Off-shell cubic hypermultiplet couplings to $\mathcal{N}=2$ higher spin gauge superfields

Abstract

We construct manifestly $4D,\mathcal{N}=2$ supersymmetric and gauge invariant off-shell cubic couplings of matter hypermultiplets to the higher integer spin gauge $\mathcal{N}=2$ multiplets introduced in arXiv:2109.07639 [hep-th]. The hypermultiplet is described by an analytic harmonic $4D,\mathcal{N}=2$ superfield $q^{+}$ with the physical component spins $\mathbf{s}=(\frac{1}{2},0)$ and an infinite number of auxiliary fields. The cubic coupling constructed has the schematic structure $q^{+}{\hat{\mathcal{H}}}_{(s)}^{++}{q}^{+}$, where ${\hat{\mathcal{H}}}_{(s)}^{++}$ is a differential analytic operator of the highest degree $(\mathbf{s}-1)$ accommodating the massless gauge $\mathcal{N}=2$ multiplet with the highest spin $\mathbf{s}$. For odd $\mathbf{s}$ the gauge group generators and couplings are proportional to $\mathrm{U}(1{)}_{PG}$ generator of the internal $\mathrm{SU}(2{)}_{PG}$ symmetry of the hypermultiplet and so do not exist if $\mathrm{SU}(2{)}_{PG}$ is unbroken. If this $\mathrm{U}(1{)}_{PG}$ is identified with the central charge of $4D,\mathcal{N}=2$ supersymmetry, a mass for the hypermultiplet is generated and the odd $\mathbf{s}$ couplings vanish in the proper massless limit. For even $\mathbf{s}$ the higher-spin gauge transformations and cubic superfield couplings can be defined for both massive and massless (central-charge neutral) hypermultiplets without including $\mathrm{U}(1{)}_{PG}$ generator. All these features directly extend to the case of $n$ hypermultiplets with the maximal internal symmetry $\mathrm{USp}(2n)\times \mathrm{SU}(2)$.

0 + 37 pages, eqs. (3.68) corrected, without any impact on the subsequent formulas and results

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• On higher-spin $\mathcal{N}=2$ supercurrent multiplets
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• Off-shell invariants of linearized $4D,\mathcal{N}=2$ supergravity in the harmonic approach
• Unconstrained $\mathcal{N}=2$ higher-spin gauge superfields and their hypermultiplet couplings
• $\mathcal{N}=2$ AdS hypermultiplets in harmonic superspace
• Unfolded hypermultiplet in harmonic superspace
• Superspace First-order Formalism for Massless Arbitrary Superspin Supermultiplets
• Novel $\mathcal{N}=2$ higher-spin supercurrents
• Diagonalization Procedure for Reducible Massless N=1 Supermultiplets
• Supersymmetry at BLTP: Recent Progress in Two Directions