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We study the theory of Weyl conformal gravity with matter degrees of freedomin a conformally invariant interaction. Specifically, we consider a triplet ofscalar fields and SO(3) non-abelian gauge fields, i.e. the Georgi-Glashow modelconformally coupled to Weyl gravity. We show that the equations of motion admitsolutions spontaneously breaking the conformal symmetry and the gauge symmetry,providing a mechanism for supplying a scale in the theory. The vacuum solutioncorresponds to anti-de-Sitter space-time, while localized soliton solutionscorrespond to magnetic monopoles in asymptotically anti-de-Sitter space-time.The resulting effective action gives rise to Einstein gravity and the residualU(1) gauge theory. This mechanism strengthens the reasons for consideringconformally invariant matter-gravity theory, which has shown promisingindications concerning the problem of missing matter in galactic rotationcurves.Comment: 20 pages, 1 figure, revised and added reference

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