Energy functionals from Conformal Gravity
Abstract
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.
- Publication:
-
Journal of High Energy Physics
- Pub Date:
- October 2022
- DOI:
- 10.1007/JHEP10(2022)123
- arXiv:
- arXiv:2209.02006
- Bibcode:
- 2022JHEP...10..123A
- Keywords:
-
- Classical Theories of Gravity;
- Gauge-Gravity Correspondence;
- Scale and Conformal Symmetries;
- High Energy Physics - Theory;
- General Relativity and Quantum Cosmology
- E-Print:
- 19 pages, 1 table, 1 figure, typo in eq.(2.8) corrected from published version