Abstract
Weyl invariant theories of scalars and gravity can generate all mass scales spontaneously, initiated by a dynamical process of ``inertial spontaneous symmetry breaking'' that does not involve a potential. This is dictated by the structure of the Weyl current, ${K}_{\ensuremath{\mu}}$, and a cosmological phase during which the Universe expands and the Einstein-Hilbert effective action is formed. Maintaining exact Weyl invariance in the renormalized quantum theory is straightforward when renormalization conditions are referred back to the VEV's of fields in the action of the theory, which implies a conserved Weyl current. We do not require scale invariant regulators. We illustrate the computation of a Weyl invariant Coleman-Weinberg potential.
Highlights
The discovery of the Higgs boson with the appearance of a fundamental, pointlike, scalar field, unaccompanied by a natural custodial symmetry, has led many authors in search of new organising principles to turn to scale symmetry
In this paper we focus on the well-known Weyl current which has been studied by many of the previous authors listed above
It is interesting to note that if we have N φi fields, the inertial symmetry breaking will yield the N − 1 φ0i fields and the dilaton which is again eaten to become the longitudinal component of Bμ, but we find that the gauge field Bμ decouples from the φ0i
Summary
The discovery of the Higgs boson with the appearance of a fundamental, pointlike, scalar field, unaccompanied by a natural custodial symmetry, has led many authors in search of new organising principles to turn to scale symmetry. There exist no fundamental mass scales, and the mass of anything is defined only relative to field VEVs in the theory For this to be phenomenologically acceptable it is necessary to explain how the spontaneous breaking of Weyl symmetry can lead to a period of inflation followed by a reheat phase and transition in the infrared to a theory describing the fundamental states of matter and their interactions with an hierarchically large difference between the Planck scale and the electroweak breaking scale. It has been shown in a simplified model involving two scalar fields that this structure is possible [2,3,7]. IV, we present a summary of our results and the conclusions to be drawn
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