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

Abstract

We propose a new gauge prepotential ${{\rm Y}}_i$ 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 ${{\rm Y}}_i$, 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 ${{\rm Y}}_i$. Our main results are also specialised to $\mathcal{N}=2$ anti-de Sitter superspace.

9 pages; V2: typos corrected; V3: published version