# Weyl symmetry and its spontaneous breaking in Standard Model and inflation

Research paper by D. M. Ghilencea, Hyun Min Lee

Indexed on: 24 Sep '18Published on: 24 Sep '18Published in: arXiv - High Energy Physics - Theory

#### Abstract

We discuss the Weyl gauge symmetry and its spontaneous breaking and apply it to model building beyond Standard Model (SM) and inflation. In models containing non-minimal couplings of the scalar fields to the Ricci scalar, that are conformal invariant, the spontaneous generation by a scalar field(s) vev (or combination thereof) of a positive Newton constant demands a negative kinetic term for the scalar field, or vice-versa. This is naturally avoided in models with additional Weyl gauge symmetry. The Weyl gauge field $\omega_\mu$, shown to couple only to the scalar sector of a SM-like Lagrangian, undergoes a Stueckelberg mechanism and becomes massive after "eating" the (radial mode) would-be-Goldstone field (dilaton $\rho$) in the scalar sector. Before the decoupling of $\omega_\mu$, the dilaton can act as UV regulator and maintain the Weyl symmetry at the quantum level, with relevance for solving the hierarchy problem. After the decoupling of $\omega_\mu$, the scalar potential depends only on the remaining (angular variables) scalar fields. A successful hilltop inflation is then possible with one of these scalar fields identified as the inflaton. While our approach is formulated in Riemannian geometry, the natural framework is that of Weyl geometry which is shown to lead to a similar Lagrangian, up to a total derivative.