High Energy Theory Seminar: Rodrigo Olea

Title: Conformal Renormalization and Energy Functionals in anti-de Sitter gravity

Abstract: We introduce a mechanism (Conformal Renormalization) to cancel divergences in Einstein gravity for asymptotically anti-de Sitter (AAdS) spaces. In the bulk, the procedure amounts to embedding Einstein gravity in Conformal Gravity, whose action is given by a conformal invariant in four dimensions. This scheme is proved to be equivalent to both holographic techniques (for physicists) and the notion of Renormalized Volume (for mathematicians).

In turn, for surfaces anchored to the conformal boundary of AAdS spaces, its area and other co-dimension 2 functionals also exhibit a divergent behavior. We show how Conformal Gravity in the bulk induces a finite surface/energy functional which, for suitable conditions, reduces to the formulas of Renormalized Area, Reduced Hawking Mass and Willmore Energy. A renormalized version of Holographic Entanglement Entropy is also discussed.

Speaker: Rodrigo Olea (Universidad Católica de Valparaíso)