Off-shell superconformal higher spin multiplets in four dimensions

TL;DR

This paper develops off-shell N=1 superconformal higher spin multiplets in four dimensions, explores their coupling to conformal supergravity, and analyzes gauge invariance conditions related to the supersymmetric Bach tensor.

Contribution

It introduces a formulation of off-shell superconformal higher spin multiplets in four dimensions and examines their coupling to conformal supergravity, including explicit examples.

Findings

Coupling of superconformal gravitino multiplet to supergravity is explicitly worked out.

The action is super-Weyl invariant for any supergravity background.

Gauge invariance requires the vanishing of the supersymmetric Bach tensor.

Abstract

We formulate off-shell N=1 superconformal higher spin multiplets in four spacetime dimensions and briefly discuss their coupling to conformal supergravity. As an example, we explicitly work out the coupling of the superconformal gravitino multiplet to conformal supergravity. The corresponding action is super-Weyl invariant for arbitrary supergravity backgrounds. However, it is gauge invariant only if the supersymmetric Bach tensor vanishes. This is similar to linearised conformal supergravity in curved background.