Spontaneous breaking of conformal invariance in theories of conformally coupled matter and Weyl gravity

TL;DR

This paper investigates how conformal symmetry can be spontaneously broken in Weyl gravity coupled with matter, leading to Einstein gravity and potential implications for dark matter phenomena.

Contribution

It demonstrates a mechanism for spontaneous conformal and gauge symmetry breaking in Weyl gravity with matter, producing Einstein gravity and residual gauge theories.

Findings

Spontaneous breaking of conformal symmetry occurs in the model.

Solutions include anti-de-Sitter space and magnetic monopoles.

The effective theory recovers Einstein gravity and U(1) gauge symmetry.

Abstract

We study the theory of Weyl conformal gravity with matter degrees of freedom in a conformally invariant interaction. Specifically, we consider a triplet of scalar fields and SO(3) non-abelian gauge fields, i.e. the Georgi-Glashow model conformally coupled to Weyl gravity. We show that the equations of motion admit solutions spontaneously breaking the conformal symmetry and the gauge symmetry, providing a mechanism for supplying a scale in the theory. The vacuum solution corresponds to anti-de-Sitter space-time, while localized soliton solutions correspond to magnetic monopoles in asymptotically anti-de-Sitter space-time. The resulting effective action gives rise to Einstein gravity and the residual U(1) gauge theory. This mechanism strengthens the reasons for considering conformally invariant matter-gravity theory, which has shown promising indications concerning the problem of missing matter in galactic rotation curves.