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

A. Edery·Luca Fabbri·M. B. Paranjape
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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.

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A. Edery, Luca Fabbri, M. B. Paranjape. 2006-05-15. Spontaneous breaking of conformal invariance in theories of conformally coupled matter and Weyl gravity. https://doi.org/10.1088/0264-9381%2F23%2F22%2F019

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