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

Abstract

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 ${\omega }_{\mu }$ becomes massive (mass $m_{\omega }\sim$ 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 ${\omega }_{\mu }$. Below $m_{\omega }$ 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 ${\varphi }_1$ (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 ${\xi }_1{\varphi }_1^2\tilde{R}$ to Weyl geometry, with Higgs mass $\propto {\xi }_1/{\xi }_0$ (${\xi }_0$ is the coefficient of the ${\tilde{R}}^2$ term). In realistic models ${\xi }_1$ must be classically tuned ${\xi }_1\ll {\xi }_0$. We comment on the quantum stability of this value.

14 pages; improved presentation (section 3)

References in corpus (5)

• Quantum scale invariance, cosmological constant and hierarchy problem
• The Higgs Phenomenon in Quantum Gravity
• Living with Ghosts and their Radiative Corrections
• Two-loop scale-invariant scalar potential and quantum effective operators
• Inflation as a spontaneous symmetry breaking of Weyl symmetry

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