Renormalized volume, extrinsic counterterms and Einstein-AdS action

Ignacio Araya (Universidad Andrés Bello, Chile)

RESUMEN: We exhibit the equivalence between the renormalized volume of AHE (asymptotically hyperbolic Einstein) manifolds and the renormalized Euclidean Einstein-AdS gravity action. The renormalization is achieved through the addition of an extrinsic counterterm at the boundary, which in the even-dimensional case corresponds to the boundary Chern form. The obtained volume is the universal part, which is finite in even dimensions and logarithmically divergent in odd dimensions. We also show that, within the AdS/CFT context, by computing the renormalized volume of certain conically singular manifolds, we can obtain the universal part of the Entanglement Entropy in the dual CFT, which naturally comes as the renormalized area of the minimal codimension-2 surface considered in the Ryu-Takayanagi construction. The renormalized EE is rewritten in terms of both topological and geometric components.