Higgs Potential from Weyl Conformal Gravity

TL;DR

This paper demonstrates how Weyl conformal gravity naturally produces a Higgs potential and mass generation for gauge fields through spontaneous symmetry breaking, linking gravity and particle physics.

Contribution

It shows that a Higgs potential emerges from Weyl gravity's $ ilde R^2$ term and that gauge invariance breaking leads to massive gauge fields, connecting gravity with Higgs physics.

Findings

Higgs potential arises from $ ilde R^2$ term in Weyl gravity.

Weyl gauge symmetry breaking absorbs Nambu-Goldstone boson, giving mass to gauge field.

Jordan and Einstein frames are gauge-equivalent via BRST formalism.

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.