$\mathcal{N}=2$ superconformal gravitino in harmonic superspace

Abstract

We present the harmonic superspace formulation of $\mathcal{N}=2$ gravitino multiplet, the simplest $\mathcal{N}=2$ half-integer spin gauge supermultiplet. It is shown that, quite similar to other $\mathcal{N}=2$ gauge multiplets, the gravitino supermultiplet is described by unconstrained analytic prepotentials $h^{++\alpha}$ and $h^{+++}$ which contain a conformal gravitino in the Wess-Zumino gauge. The analytic prepotentials naturally come out from the study of $\mathcal{N}=2$ supercurrents associated with hidden symmetries of $\mathcal{N}=2$ vector-hypermultiplet system. We construct the covariant $\mathcal{N}=2$ superfield strengths and the invariant $\mathcal{N}=2$ superfield actions and sketch their component contents. We observe that, at cost of introducing new auxiliary coordinates $\Psi^\alpha$ and $\omega^+$, the gravitino analytic prepotentials acquire a nice geometric interpretation as extra veilbeins of the covariant harmonic derivative $\mathfrak{D}^{++}$. We speculate on a possible origin of the additional coordinates, including their relationship with $\mathcal{N}=2$ supertwistors.