On conformal higher spin wave operators

TL;DR

This paper investigates conformal higher spin wave operators in various backgrounds, revealing their non-factorization in general and providing explicit factorizations in specific cases, advancing understanding of their structure.

Contribution

It demonstrates the non-factorization of conformal higher spin wave operators in general backgrounds and offers explicit factorizations on (A)dS and Einstein backgrounds, including a specific fix in four dimensions.

Findings

Wave operators generally do not factorize.

Explicit factorized forms are provided for (A)dS backgrounds.

A fix for the s=3 wave operator in d=4 on Bach-flat backgrounds.

Abstract

We analyze free conformal higher spin actions and the corresponding wave operators in arbitrary even dimensions and backgrounds. We show that the wave operators do not factorize in general, and identify the Weyl tensor and its derivatives as the obstruction to factorization. We give a manifestly factorized form for them on (A)dS backgrounds for arbitrary spin and on Einstein backgrounds for spin 2. We are also able to fix the conformal wave operator in d=4 for s=3 up to linear order in the Riemann tensor on generic Bach-flat backgrounds.