Geometrical structure of Weyl invariants for spin three gauge field in general gravitational background in $d=4$

Abstract

We construct all possible Weyl invariant actions in $d=4$ for linearized spin three field in a general gravitational background. The first action is obtained as the square of the generalized Weyl tensor for a spin three gauge field in nonlinear gravitational background. It is, however, not invariant under spin three gauge transformations. We then construct two other nontrivial Weyl but not gauge invariant actions which are linear in the Weyl tensor of the background geometry. We then discuss existence and uniqueness of a possible linear combination of these three actions which is gauge invariant. We do this at the linear order in the background curvature for Ricci flat backgrounds.

arXiv comment32 pages, v.2, misprints corrected

References in corpus (29)

• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• Einstein Gravity from Conformal Gravity
• Conformal Higher Spin Theory
• Conformal Higher Spin Symmetries of 4d Massless Supermultiplets and $osp(L,2M)$ Invariant Equations in Generalized (Super)Space
• Effective action in a higher-spin background
• On partition function and Weyl anomaly of conformal higher spin fields
• Bosonic conformal higher--spin fields of any symmetry
• Classical and quantum stability of higher-derivative dynamics
• Partition function of free conformal higher spin theory
• Higher-spin current multiplets in operator-product expansions
• Partially-massless higher-spin algebras and their finite-dimensional truncations
• Theory of higher spin tensor currents and central charges
• Ordinary-derivative formulation of conformal totally symmetric arbitrary spin bosonic fields
• On triviality of S-matrix in conformal higher spin theory
• On conformal higher spin wave operators
• Arbitrary spin conformal fields in (A)dS
• A note on higher-derivative actions for free higher-spin fields
• Notes on higher-spin algebras: minimal representations and structure constants
• Conformal Coupling of Higher Spin Gauge Fields to a Scalar Field in $Ad{S}_4$ and Generalized Weyl Invariance
• Conformal invariant interaction of a scalar field with the higher spin field in AdS_{D}
• On induced action for conformal higher spins in curved background
• Weyl Action of Two-Column Mixed-Symmetry Field and Its Factorization Around (A)dS Space
• On conformal higher spins in curved background
• On Higher Spin Symmetries in AdS_{5}
• The quantum one loop trace anomaly of the higher spin conformal conserved currents in the bulk of $Ad{S}_4$
• The structure of the trace anomaly of higher spin conformal currents in the bulk of $Ad{S}_4$
• Higher-derivative massive actions from dimensional reduction
• BRST-BV approach to conformal fields
• General light-cone gauge approach to conformal fields and applications to scalar and vector fields

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• $\mathcal{N}=2$ superconformal higher-spin multiplets and their hypermultiplet couplings
• Generalised conformal higher-spin fields in curved backgrounds
• Generalised superconformal higher-spin multiplets
• Higher-spin Cotton tensors and massive gauge-invariant actions in AdS${}_3$
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