On the structure of the conformal higher-spin wave operators

TL;DR

This paper derives a systematic, factorized form of conformal higher spin wave operators on constant curvature backgrounds, revealing their gauge invariance structure and relation to tractor calculus for arbitrary integer spins and gauge invariance orders.

Contribution

It provides the first explicit factorization formulas for CHS wave operators with higher gauge invariance orders, extending known results for Fradkin-Tseytlin fields.

Findings

Derived explicit factorization formulas for CHS wave operators with arbitrary spin and gauge invariance order.

Established a detailed relationship between CHS gauge invariance and partially gauge-fixed wave operators.

Connected the tractor approach with the structure of CHS equations and gauge symmetries.

Abstract

We study conformal higher spin (CHS) fields on constant curvature backgrounds. By employing parent formulation technique in combination with tractor description of GJMS operators we find a manifestly factorized form of the CHS wave operators for symmetric fields of arbitrary integer spin $s$ and gauge invariance of arbitrary order $t\leq s$. In the case of the usual Fradkin-Tseytlin fields $t=1$ this gives a systematic derivation of the factorization formulas known in the literature while for $t>1$ the explicit formulas were not known. We also relate the gauge invariance of the CHS fields to the partially-fixed gauge invariance of the factors and show that the factors can be identified with (partially gauge-fixed) wave operators for (partially)-massless or special massive fields. As a byproduct, we establish a detailed relationship with the tractor approach and, in particular, derive the tractor form of the CHS equations and gauge symmetries.