TY - JOUR

T1 - Matching one-loop divergences in 7D Einstein and 6D Conformal Gravities

AU - Aros, Rodrigo

AU - Bugini, Fabrizzio

AU - Díaz, Danilo E.

N1 - Funding Information:
information Universidad Andres Bello (UNAB) DI 14-18/REG, Universidad Andres Bello (UNAB) DI 08-19/REGWe thank Y. Matsumoto, K. Mkrtchyan, and A. Tseytlin for valuable discussions. The work of R.A. was supported in part by grant UNAB DI 08-19/REG. D.E.D. acknowledges support by grant UNAB DI 14-18/REG and is also grateful for the hospitality during the symposium STARS2019.

PY - 2019/11/1

Y1 - 2019/11/1

N2 - Within the context of AdS/CFT correspondence, we first compute the one-loop infrared (IR) divergences of 7D Einstein gravity in a certain Poincaré-Einstein background metric. Then, we compute the one-loop ultraviolet (UV) divergences of 6D conformal gravity on the conformal boundary. We verify the equality of the above results that stem from the IR–UV connection of the duality dictionary. Key ingredients are heat kernel techniques, factorization of the boundary higher-derivative kinetic operator for the Weyl graviton on the 6D Einstein metric, and Wentzel–Kramers–Brillouin (WKB) exactness of the Einstein graviton in the chosen 7D Poincaré-Einstein background. Overall, we elucidate the way in which the 6D results containing the type-A and type-B conformal anomalies for the Weyl graviton are encoded in the 7D “hologram” given by the fluctuation determinant for the Einstein graviton. We finally discuss possible extensions to include higher-spin fields.

AB - Within the context of AdS/CFT correspondence, we first compute the one-loop infrared (IR) divergences of 7D Einstein gravity in a certain Poincaré-Einstein background metric. Then, we compute the one-loop ultraviolet (UV) divergences of 6D conformal gravity on the conformal boundary. We verify the equality of the above results that stem from the IR–UV connection of the duality dictionary. Key ingredients are heat kernel techniques, factorization of the boundary higher-derivative kinetic operator for the Weyl graviton on the 6D Einstein metric, and Wentzel–Kramers–Brillouin (WKB) exactness of the Einstein graviton in the chosen 7D Poincaré-Einstein background. Overall, we elucidate the way in which the 6D results containing the type-A and type-B conformal anomalies for the Weyl graviton are encoded in the 7D “hologram” given by the fluctuation determinant for the Einstein graviton. We finally discuss possible extensions to include higher-spin fields.

KW - AdS/CFT correspondence

KW - anomalies in quantum field theory

UR - http://www.scopus.com/inward/record.url?scp=85077839708&partnerID=8YFLogxK

U2 - 10.1002/asna.201913746

DO - 10.1002/asna.201913746

M3 - Article

AN - SCOPUS:85077839708

VL - 340

SP - 1008

EP - 1012

JO - Astronomische Nachrichten

JF - Astronomische Nachrichten

SN - 0004-6337

IS - 9-10

ER -