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

TL;DR

This paper introduces a new gauge prepotential for the ${ m extbf{N}=2}$ superconformal gravitino multiplet, derived from superspace reduction, and constructs a gauge-invariant action applicable in conformally-flat backgrounds.

Contribution

It proposes a novel gauge prepotential $B6_i$ for the ${ m extbf{N}=2}$ superconformal gravitino multiplet, derived via superspace reduction from ${ m extbf{N}=3}$ supergravity, and develops a superprojector and invariant action.

Findings

Introduced a new gauge prepotential $6_i$ for the ${ m extbf{N}=2}$ superconformal gravitino multiplet.

Derived a superprojector mapping superfields to conformal supercurrents.

Constructed a superconformal chiral action invariant in conformally-flat backgrounds.

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.