Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs
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 g...
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doaj-ced07b9dfb1b4738ba2729aa83325bba2020-11-25T03:59:13ZengSpringerOpenJournal of High Energy Physics1029-84792019-10-0120191015910.1007/JHEP10(2019)221Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTsGiorgos Anastasiou0Ignacio J. Araya1Alberto Güijosa2Rodrigo Olea3Instituto de Física, Pontificia Universidad Católica de ValparaísoDepartamento de Ciencias Físicas, Universidad Andres BelloDepartamento de Física de Altas Energías, Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de MéxicoDepartamento de Ciencias Físicas, Universidad Andres BelloAbstract 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 B d 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.http://link.springer.com/article/10.1007/JHEP10(2019)221AdS-CFT CorrespondenceClassical Theories of GravityGauge-gravity correspondence |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Giorgos Anastasiou Ignacio J. Araya Alberto Güijosa Rodrigo Olea |
spellingShingle |
Giorgos Anastasiou Ignacio J. Araya Alberto Güijosa Rodrigo Olea Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs Journal of High Energy Physics AdS-CFT Correspondence Classical Theories of Gravity Gauge-gravity correspondence |
author_facet |
Giorgos Anastasiou Ignacio J. Araya Alberto Güijosa Rodrigo Olea |
author_sort |
Giorgos Anastasiou |
title |
Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs |
title_short |
Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs |
title_full |
Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs |
title_fullStr |
Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs |
title_full_unstemmed |
Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs |
title_sort |
renormalized ads gravity and holographic entanglement entropy of even-dimensional cfts |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2019-10-01 |
description |
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 B d 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. |
topic |
AdS-CFT Correspondence Classical Theories of Gravity Gauge-gravity correspondence |
url |
http://link.springer.com/article/10.1007/JHEP10(2019)221 |
work_keys_str_mv |
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1724455088466952192 |