Abstract
We discuss the local (gauged) Weyl symmetry and its spontaneous breaking and apply it to model building beyond the Standard Model (SM) and inflation. In models with non-minimal couplings of the scalar fields to the Ricci scalar, that are conformal invariant, the spontaneous generation by a scalar field(s) vev 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 $\omega_\mu$ couples to the scalar sector but not to the fermionic sector of a SM-like Lagrangian. The field $\omega_\mu$ 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 {\it 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, that can be the Higgs field, inflaton, etc. We show that successful inflation is then possible with one of these scalar fields identified as the inflaton. While our approach is derived in the Riemannian geometry with $\omega_\mu$ introduced to avoid ghosts, the natural framework is that of Weyl geometry which for the same matter spectrum is shown to generate the same Lagrangian, up to a total derivative.
Highlights
In this paper, we discuss the Weyl gauge symmetry and its spontaneous breaking together with its implications for model building beyond the standard model (SM) and for inflation.One phenomenological motivation relates to the observation that the SM with a Higgs mass parameter set to zero has a classical scale symmetry [1]
If this symmetry is preserved at the quantum level by UV regularization as in [2,3,4,5,6,7] and is broken spontaneously only, it can naturally protect at the quantum level a hierarchy of fields vacuum expectation values (VEVs) of the theory [3,6,8,9,10]
The hierarchy we refer to is that between the Higgs field VEV and that of new physics represented by the VEV of the flat direction associated with global scale symmetry breaking
Summary
We discuss the Weyl gauge symmetry and its spontaneous breaking together with its implications for model building beyond the standard model (SM) and for inflation. Demanding the theory be conformal invariant and spontaneous-only breaking of the conformal symmetry leads to a negative kinetic term for the corresponding scalar field, a nuisance that is often quietly glided over. This problem is automatically avoided in models with Weyl gauge symmetry [14,16] and motivated our study of this symmetry in Secs.
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