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We implement quantum corrections for a magnetic monopole in a classicallyconformally invariant theory containing gravity. This yields the trace(conformal) anomaly and introduces a length scale in a natural fashion via theprocess of renormalization. We evaluate the one-loop effective potential andextract the vacuum expectation value (VEV) from it; spontaneous symmetrybreaking is radiatively induced. The VEV is set at the renormalization scale$M$ and we exchange the dimensionless scalar coupling constant for thedimensionful VEV via dimensional transmutation. The asymptotic (background)spacetime is anti-de Sitter (AdS) and its Ricci scalar is determined entirelyby the VEV. We obtain analytical asymptotic solutions to the coupled set ofequations governing gravitational, gauge and scalar fields that yield themagnetic monopole in an AdS spacetime.

Radiatively induced symmetry breaking and the conformally coupled magnetic monopole in AdS space