Spontaneous breaking of Weyl quadratic gravity to Einstein action and Higgs potential

  • D. M. GhilenceaEmail author
Open Access
Regular Article - Theoretical Physics


We consider the (gauged) Weyl gravity action, quadratic in the scalar curvature (\( \tilde{R} \)) and in the Weyl tensor (\( {\tilde{C}}_{\mu \nu \rho \sigma} \)) of the Weyl conformal geometry. In the absence of matter fields, this action has spontaneous breaking in which the Weyl gauge field ωμ becomes massive (mass mω ∼ Planck scale) after “eating” the dilaton in the \( \tilde{R} \)2 term, in a Stueckelberg mechanism. As a result, one recovers the Einstein-Hilbert action with a positive cosmological constant and the Proca action for the massive Weyl gauge field ωμ. Below mω this field decouples and Weyl geometry becomes Riemannian. The Einstein-Hilbert action is then just a “low-energy” limit of Weyl quadratic gravity which thus avoids its previous, long-held criticisms. In the presence of matter scalar field ϕ1 (Higgs-like), with couplings allowed by Weyl gauge symmetry, after its spontaneous breaking one obtains in addition, at low scales, a Higgs potential with spontaneous electroweak symmetry breaking. This is induced by the non-minimal coupling \( {\xi}_1{\phi}_1^2\tilde{R} \) to Weyl geometry, with Higgs mass ∝ ξ100 is the coefficient of the \( \tilde{R} \)2 term). In realistic models ξ1 must be classically tuned ξ1 ≪ ξ0. We comment on the quantum stability of this value.


Classical Theories of Gravity Effective Field Theories Higgs Physics Spontaneous Symmetry Breaking 


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© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of Theoretical PhysicsNational Institute of Physics and Nuclear EngineeringBucharestRomania

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