N=2 superconformal gravitino in harmonic superspace

Abstract

We present the harmonic superspace formulation of $N=2$ gravitino multiplet, the simplest $N=2$ half-integer spin gauge supermultiplet. It is shown that, quite similar to other $N=2$ 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 $N=2$ supercurrents associated with hidden symmetries of $N=2$ vector-hypermultiplet system. We construct the covariant $N=2$ superfield strengths and the invariant $N=2$ 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 vielbeins of the covariant harmonic derivative $D^{++}$. We speculate on a possible origin of the additional coordinates, including their relationship with $N=2$ supertwistors.