Generalised conformal higher-spin fields in curved backgrounds

TL;DR

This paper develops gauge-invariant models for conformal higher-spin fields of spins 5/2 and 3 in four-dimensional curved backgrounds, revealing the necessity of lower-spin fields for gauge invariance beyond spin 2.

Contribution

It constructs the first gauge-invariant models for conformal maximal depth higher-spin fields in curved backgrounds, confirming the need for lower-spin fields for gauge invariance.

Findings

Gauge-invariant models for spins 5/2 and 3 in Bach-flat backgrounds.

Lower-spin fields are required for gauge invariance when spin > 2.

Supports earlier conjectures about conformal higher-spin fields of minimal depth.

Abstract

The problem of constructing gauge-invariant actions for conformal higher-spin fields in curved backgrounds is known to be notoriously difficult. In this paper we present gauge-invariant models for conformal maximal depth fields with spin $s=5/2$ and $s=3$ in four-dimensional Bach-flat backgrounds. We find that certain lower-spin fields must be introduced to ensure gauge invariance when $s>2$, which is analogous to a conjecture made earlier in the literature for conformal higher-spin fields of minimal depth.