Matching one‐loop divergences in 7D Einstein and 6D Conformal Gravities

Abstract

Within the context of AdS/CFT correspondence, we first compute the one-loopinfrared (IR) divergences of 7D Einstein gravity in a certain Poincaré-Einsteinbackground metric. Then, we compute the one-loop ultraviolet (UV) diver-gences of 6D conformal gravity on the conformal boundary. We verify theequality of the above results that stem from the IR–UV connection of the dual-ity dictionary. Key ingredients are heat kernel techniques, factorization of theboundary higher-derivative kinetic operator for the Weyl graviton on the 6D Ein-stein metric, and Wentzel–Kramers–Brillouin (WKB) exactness of the Einsteingraviton in the chosen 7D Poincaré-Einstein background. Overall, we elucidatethe way in which the 6D results containing the type-A and type-B conformalanomalies for the Weyl graviton are encoded in the 7D “hologram” given by thefluctuation determinant for the Einstein graviton. We finally discuss possibleextensions to include higher-spin fields.