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

Rodrigo Aros, Fabrizzio Bugini, Danilo E. Díaz

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1008-1012
Number of pages5
JournalAstronomische Nachrichten
Issue number9-10
Publication statusPublished - 1 Nov 2019


  • AdS/CFT correspondence
  • anomalies in quantum field theory

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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