Conformal anomaly in the gravitationally coupled magnetic monopole and vacua effects under external conditions

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We apply the techniques of quantum field theory to different physical systems under various external conditions. Our first system consists of a Georgi-Glashow model (composed of a triplet of scalar fields and SO(3) non-Abelian gauge fields) conformally coupled to gravity. We have already shown in a previous work that magnetic monopole solutions in asymptotically Anti-de Sitter (AdS) spacetime exist in this system. In this proposal we break the conformal symmetry by adding quantum matter corrections to the action leading to the conformal anomaly. Our preliminary analysis shows that an Einstein-Hilbert term (General Relativity), a cosmological constant and massive scalars, which do not appear in the original action, emerge after an expansion of the action about the non-trivial vacuum and dominate the low energy or long distance regime. The conformal anomaly fixes the scale and we anticipate that the gravitational constant G, the cosmological constant and the mass of the scalars can be expressed in terms of the parameters of the theory.