Higgs and gravitational scalar fields together induce Weyl gauge

Abstract

A common biquadratic potential for the Higgs field $h$ and an additional scalar field $\varphi$, non minimally coupled to gravity, is considered in locally scale symmetric approaches to standard model fields in curved spacetime. A common ground state of the two scalar fields exists and couples both fields to gravity, more precisely to scalar curvature $R$. In Einstein gauge ($\varphi =const$, often called "Einstein frame"), also $R$ is scaled to a constant. This condition makes perfect sense, even in the general case, in the Weyl geometric approach. There it has been called {\em Weyl gauge}, because it was first considered by Weyl in the different context of his original scale geometric theory of gravity of 1918. Now it seems to get new meaning as a combined effect of electroweak theory and gravity, and their common influence on atomic frequencies.

11 pp

References in corpus (4)

• Conformal Symmetry and the Standard Model
• Scale invariance, unimodular gravity and dark energy
• Implication of Compensator Field and Local Scale Invariance in the Standard Model
• Geometric realizations, curvature decompositions, and Weyl manifolds

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• Inflation in Weyl Scaling Invariant Gravity with $R^3$ Extensions
• Inflation in light of ACT/SPT: A new perspective from Weyl gravity
• Metric Measure Space as a Framework for Gravitation