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.Comment: 20 pages, 1 figure, revised and added reference
