# Renormalized Volume/Area from Conformal Gravity

### APA

Olea, R. (2024). Renormalized Volume/Area from Conformal Gravity. Perimeter Institute. https://pirsa.org/24020099

### MLA

Olea, Rodrigo. Renormalized Volume/Area from Conformal Gravity. Perimeter Institute, Feb. 29, 2024, https://pirsa.org/24020099

### BibTex

@misc{ pirsa_PIRSA:24020099, doi = {10.48660/24020099}, url = {https://pirsa.org/24020099}, author = {Olea, Rodrigo}, keywords = {Quantum Gravity}, language = {en}, title = {Renormalized Volume/Area from Conformal Gravity}, publisher = {Perimeter Institute}, year = {2024}, month = {feb}, note = {PIRSA:24020099 see, \url{https://pirsa.org}} }

Rodrigo Olea Universidad Nacional Andres Bello

## Abstract

We explore the physical consequences of embedding Einstein gravity with negative cosmological constant in Conformal Gravity in four dimensions. In the bulk, the procedure is equivalent to Holographic Renormalization, as the Einstein-AdS action appears augmented by the correct boundary counterterms. In codimension-2, 4D Conformal Gravity induces a 2D conformal invariant, which leads to a renormalized area for minimal surfaces attached to the conformal boundary. For arbitrary surfaces, this proposal reproduces other energy functionals as Willmore Energy and Reduced Hawking Mass. In particular, this procedure provides a more geometric approach to the computation of Holographic Entanglement Entropy for CFTs dual to 4D Einstein gravity.

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