On induced action for conformal higher spins in curved background

Abstract

We continue the investigation of the structure of the action for a tower of conformal higher spin fields in non-trivial 4d background metric recently discussed in arXiv:1609.09381. The action is defined as an induced one from path integral of a conformal scalar field in curved background coupled to higher spin fields. We analyse in detail the dependence of the quadratic part of the induced action on the spin 1 and spin 3 fields, determining the presence of a curvature-dependent mixed spin 1 - spin 3 term. One consequence is that the pure spin 3 kinetic term cannot be gauge-invariant on its own beyond the leading term in small curvature expansion. We also compute the non-zero contribution of the 1-3 mixing term to the conformal anomaly c-coefficient. One is thus to determine all such mixing terms before addressing the question of possible vanishing of the total c-coefficient in the conformal higher spin theory.

27 pages, v2 typos corrected

References in corpus (5)

• Effective action in a higher-spin background
• Partition function of free conformal higher spin theory
• On triviality of S-matrix in conformal higher spin theory
• On conformal higher spin wave operators
• Arbitrary spin conformal fields in (A)dS

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• Symmetries of supergravity backgrounds and supersymmetric field theory
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• Scattering of conformal higher spin fields
• New locally (super)conformal gauge models in Bach-flat backgrounds
• Conformal interactions between matter and higher-spin (super)fields
• Conformal Higher-Spin Gravity: Linearized Spectrum = Symmetry Algebra
• $\mathcal{N}=2$ superconformal higher-spin multiplets and their hypermultiplet couplings
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• Geometrical structure of Weyl invariants for spin three gauge field in general gravitational background in $d=4$
• Generalised conformal higher-spin fields in curved backgrounds
• Generalised superconformal higher-spin multiplets
• Higher-spin Cotton tensors and massive gauge-invariant actions in AdS${}_3$
• On the Weyl anomaly of 4D Conformal Higher Spins: a holographic approach
• Induced action for superconformal higher-spin multiplets using SCFT techniques
• Induced Action for Conformal Higher Spins from Worldline Path Integrals
• The Weyl Anomaly from the 6D Superconformal Index