On the structure of the conformal higher-spin wave operators

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 $t\le s$. 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.

arXiv comment28 pages

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Cited by in corpus (9)

• Conformal geometry and (super)conformal higher-spin gauge theories
• An embedding formalism for CFTs in general states on curved backgrounds
• Spin projection operators in (A)dS and partial masslessness
• AdS superprojectors
• Generalised conformal higher-spin fields in curved backgrounds
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• Higher-spin Cotton tensors and massive gauge-invariant actions in AdS${}_3$
• Conformal Lagrangians from the (formal) near boundary analysis of AdS gauge fields
• GJMS-like operators on symmetric 2-tensors and their gravitational duals