The $\mathcal{N}=2$ superconformal gravitino multiplet

Abstract

We propose a new gauge prepotential $\Upsilon_i$ describing the four-dimensional ${\mathcal N}=2$ superconformal gravitino multiplet. The former naturally arises via a superspace reduction of the ${\mathcal N}=3$ conformal supergravity multiplet. A locally superconformal chiral action for $\Upsilon_i$, which is gauge-invariant in arbitrary conformally-flat backgrounds, is derived. This construction readily yields a new superprojector, which maps an isospinor superfield $\Psi_i$ to a multiplet characterised by the properties of a conformal supercurrent associated with $\Upsilon_i$. Our main results are also specialised to ${\mathcal N}=2$ anti-de Sitter superspace.