Higgs Potential from Weyl Conformal Gravity

Abstract

We consider Weyl's conformal gravity coupled to a complex matter field in Weyl geometry. It is shown that a Higgs potential naturally arises from a ${\tilde{R}}^2$ term in moving from the Jordan frame to the Einstein frame. A massless Nambu-Goldstone boson, which stems from spontaneous symmetry breakdown of the Weyl gauge invariance, is absorbed into the Weyl gauge field, thereby the gauge field becoming massive. We present a model where the gravitational interaction generates a Higgs potential whose form is a perfect square. Finally, we show that a theory in the Jordan frame is gauge-equivalent to the corresponding theory in the Einstein frame via the BRST formalism.

18 pages

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• Quadratic Gravity and Restricted Weyl Symmetry
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• Inflation in light of ACT/SPT: A new perspective from Weyl gravity