Generalised conformal higher-spin fields in curved backgrounds

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.

20 pages; v2: comments and references added; v3: published version

References in corpus (19)

• Conformal Higher Spin Theory
• Effective action in a higher-spin background
• Geometric Formulation for Partially Massless Fields
• Weyl-Gauging and Conformal Invariance
• Higher order singletons, partially massless fields and their boundary values in the ambient approach
• On limits of superstring in AdS_5 x S^5
• Bosonic conformal higher--spin fields of any symmetry
• On higher spin interactions with matter
• Conformal supergravity in three dimensions: New off-shell formulation
• Conformal Invariance of Partially Massless Higher Spins
• Conformal Operators for Partially Massless States
• Conformally Covariant Differential Operators: Symmetric Tensor Fields
• New Conformal Higher Spin Gravities in $3d$
• Off-shell superconformal higher spin multiplets in four dimensions
• On conformal higher spin wave operators
• On induced action for conformal higher spins in curved background
• Conformal geometry and (super)conformal higher-spin gauge theories
• On the structure of the conformal higher-spin wave operators
• Geometrical structure of Weyl invariants for spin three gauge field in general gravitational background in $d=4$

Cited by in corpus (5)

• Extended superconformal higher-spin gauge theories in four dimensions
• New locally (super)conformal gauge models in Bach-flat backgrounds
• $\mathcal{N}=2$ superconformal higher-spin multiplets and their hypermultiplet couplings
• Generalised superconformal higher-spin multiplets
• GJMS-like operators on symmetric 2-tensors and their gravitational duals