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Journal of High Energy Physics

, 2019:221 | Cite as

Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs

  • Giorgos Anastasiou
  • Ignacio J. ArayaEmail author
  • Alberto Güijosa
  • Rodrigo Olea
Open Access
Regular Article - Theoretical Physics
  • 21 Downloads

Abstract

We derive a general formula for renormalized entanglement entropy in even- dimensional CFTs holographically dual to Einstein gravity in one dimension higher. In order to renormalize, we adapt the Kounterterm method to asymptotically locally AdS manifolds with conical singularities. On the gravity side, the computation considers extrin- sic counterterms and the use of the replica trick à la Lewkowycz-Maldacena. The boundary counterterm Bd is shown to satisfy a key property, in direct analogy to the Euler density: when evaluated on a conically singular manifold, it decomposes into a regular part plus a codimension-2 version of itself located at the conical singularity. The renormalized entropy thus obtained is shown to correspond to the universal part of the holographic entangle- ment entropy, which for spherical entangling surfaces is proportional to the central charge a that is the subject of the a-theorem. We also review and elucidate various aspects of the Kounterterm approach, including in particular its full compatibility with the Dirichlet condition for the metric at the conformal boundary, that is of standard use in holography.

Keywords

AdS-CFT Correspondence Classical Theories of Gravity Gauge-gravity correspondence 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

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© The Author(s) 2019

Authors and Affiliations

  1. 1.Instituto de FísicaPontificia Universidad Católica de ValparaísoValparaísoChile
  2. 2.Departamento de Ciencias FísicasUniversidad Andres BelloSantiagoChile
  3. 3.Departamento de Física de Altas Energías, Instituto de Ciencias NuclearesUniversidad Nacional Autónoma de MéxicoCDMXMexico

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