Energy functionals from Conformal Gravity

Giorgos Anastasiou, Ignacio J. Araya, Rodrigo Olea

Research output: Contribution to journalArticlepeer-review


We provide a new derivation of the Hawking mass and Willmore energy functionals for asymptotically AdS spacetimes, by embedding Einstein-AdS gravity in Conformal Gravity. By construction, the evaluation of the four-dimensional Conformal Gravity action in a manifold with a conical defect produces a codimension-2 conformal invariant functional LΣ. The energy functionals are then particular cases of LΣ for Einstein-AdS and pure AdS ambient spaces, respectively. The bulk action is finite for AdS asymptotics and both Hawking mass and Willmore energy are finite as well. The result suggests a generic relation between conformal invariance and renormalization, where the codimension-2 properties are inherited from the bulk gravity action.

Original languageEnglish
Article number123
JournalJournal of High Energy Physics
Issue number10
Publication statusPublished - Oct 2022


  • Classical Theories of Gravity
  • Gauge-Gravity Correspondence
  • Scale and Conformal Symmetries

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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