# Spontaneous breaking of Weyl conformal gravity to Einstein action and Higgs potential

Research paper by D. M. Ghilencea

Indexed on: 20 Dec '18Published on: 20 Dec '18Published in: arXiv - High Energy Physics - Theory

#### Abstract

We consider the local (gauged) Weyl action, quadratic in the scalar curvature ($\tilde R$) and in the Weyl tensor ($\tilde C_{\mu\nu\rho\sigma}$) of Weyl's conformal geometry. In the absence of matter fields, this action can have spontaneous breaking that recovers the Einstein-Hilbert action below the mass of the Weyl gauge field ($\omega_\mu$), with a positive cosmological constant. The field $\omega_\mu$ becomes massive after "eating" the dilaton in the $\tilde R^2$ term, in a Stueckelberg-like mechanism, then decouples (near Planck scale) and Riemannian geometry is recovered. In the presence of matter (Higgs-like) scalar field ($\phi_1$) with all couplings allowed by local Weyl symmetry, after its spontaneous breaking one is left with a massive Weyl gauge field and a Higgs potential that has spontaneous electroweak symmetry breaking. This is induced by the Higgs non-minimal coupling $\xi_1\tilde R \phi_1^2$ 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 to values $\xi_1\ll\xi_0$. We comment on the quantum stability of this value.