Conformal renormalization of scalar-tensor theories

Abstract

We study a conformally coupled scalar-tensor theory with a quartic potential possessing local conformal symmetry up to a boundary term. We show that requiring the restoration of the full local conformal symmetry fixes the counterterms that render the on-shell action finite. The building block of the resulting action is a conformally covariant tensor which is constructed out of the metric and the scalar field and it has the same conformal weight as the Weyl tensor. This allows us to obtain the counterterms for the scalar-tensor sector in a closed form. The finiteness of the conformally complete version of the action is suggestive on the validity of the Conformal Renormalization prescription. We extend this theory by adding the Conformal Gravity action and also the Einstein-AdS action written in McDowell-Mansouri form. Even though the latter breaks the conformal symmetry, we find that the action is still renormalized provided a suitable falloff of the scalar field when considering asymptotically locally anti-de Sitter solutions. Black hole solutions in these theories are studied, for which the Hawking temperature and the partition function to first order in the saddle-point approximation are calculated, providing a concrete example of this renormalization scheme.

28 pages, accepted in PRD

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Cited by in corpus (9)

• On the Ghost Problem of Conformal Gravity
• Nonlinearly charging the conformally dressed black holes preserving duality and conformal invariance
• Conformal Renormalization of topological black holes in AdS${}_6$
• Holographic renormalization of Horndeski gravity
• Electric/magnetic duality of dyonic Kerr-Newman-NUT-AdS spacetimes
• Asymptotically AdS black hole with a conformally-coupled scalar field in the first-order formalism of gravity
• Non-Abelian black holes in conformal gravity
• A study about black hole solutions with nonconstant transversal curvature and its conserved charges in Lovelock gravity
• Nonconformally Ricci-flat instantons in Conformal Gravity with and without nonlinear matter fields