Anastasiou, G.Araya, I.J.Arias, C.Olea, R.2019-11-292019-11-292018-08Journal of High Energy Physics, 2018(8), art. no. 136.1126-6708DOI: 10.1007/JHEP08(2018)136http://repositorio.unab.cl/xmlui/handle/ria/10940Indexación: Scopus.The authors thank D.E. Díaz, P. Sundell and A. Waldron for interesting discussions. C.A. is a Universidad Andres Bello (UNAB) Ph.D. Scholarship holder, and his work is supported by Dirección General de Investigación (DGI-UNAB). This work is funded in part by FONDECYT Grants No. 1170765 “Boundary dynamics in anti-de Sitter gravity and gauge/gravity duality ” and No. 3180620 “Entanglement Entropy and AdS gravity ”, and CONICYT Grant DPI 20140115.We exhibit the equivalence between the renormalized volume of asymptotically anti-de Sitter (AAdS) Einstein manifolds in four and six dimensions, and their renormalized Euclidean bulk gravity actions. The action is that of Einstein gravity, where the renormalization is achieved through the addition of a single topological term. We generalize this equivalence, proposing an explicit form for the renormalized volume of higher even-dimensional AAdS Einstein manifolds. We also show that evaluating the renormalized bulk gravity action on the conically singular manifold of the replica trick results in an action principle that corresponds to the renormalized volume of the regular part of the bulk, plus the renormalized area of a codimension-2 cosmic brane whose tension is related to the replica index. Renormalized Rényi entropy of odd-dimensional holographic CFTs can thus be obtained from the renormalized area of the brane with finite tension, including the effects of its backreaction on the bulk geometry. The area computation corresponds to an extremization problem for an enclosing surface that extends to the AdS boundary, where the newly defined renormalized volume is considered. © 2018, The Author(s).enAdS-CFT CorrespondenceClassical Theories of GravityGauge-gravity correspondenceArtículo