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Renormalization of scalar-tensor AdS gravity theories in 6D
(2025) Osorio Navarro, Loreto Soledad; Araya, Ignacio ; Bañados Lira, Maximo; Pontificia Universidad Católica de Chile. Facultad de Física
In this work we consider a scalar-tensor gravity action in six dimensions and study its finiteness through conformal renormalization. This action comprises a purely metric sector, defined by renormalized Einstein gravity, coupled to a scalar sector derived from the Lovelock gravity scalar uplift in six dimensions. For static black holes with both conformally flat and non-conformally flat transverse sections, the renormalized action yields finite results. In conformally flat cases, finiteness is achieved solely through a topological Euler term with a specific coupling. For non-conformally flat transverse sections, an additional boundary current term with a distinct coupling is required tocancel subleading divergences. These couplings match those derived from purely metric conformal embeddings in six dimensions, validating consistency across frameworks.The results indicate that starting from renormalized Lovelock theory, one can use the scalar conformal uplift to obtain a renormalized scalar-tensor theory with a non-minimally coupled scalar, thus extending conformal renormalization as a procedure to cases with (conformally coupled) matter.