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We extend our topological renormalization scheme for Entanglement Entropy toholographic CFTs of arbitrary odd dimensions in the context of the AdS/CFTcorrespondence. The procedure consists in adding the Chern form as a boundaryterm to the area functional of the Ryu-Takayanagi minimal surface. Therenormalized Entanglement Entropy thus obtained can be rewritten in terms ofthe Euler characteristic and the AdS curvature of the minimal surface. Thisprescription considers the use of the Replica Trick to express the renormalizedEntanglement Entropy in terms of the renormalized gravitational actionevaluated on the conically-singular replica manifold extended to the bulk. Thisrenormalized action is obtained in turn by adding the Chern form as thecounterterm at the boundary of the 2n-dimensional asymptotically AdS bulkmanifold. We explicitly show that, up to next-to-leading order in theholographic radial coordinate, the addition of this boundary term cancels thedivergent part of the Entanglement Entropy. We discuss possible applications ofthe method for studying CFT parameters like central charges.

Topological terms, AdS_2n gravity and renormalized Entanglement Entropy of holographic CFTs