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

Abstract

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