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

Giorgos Anastasiou, Ignacio J. Araya, Alberto Güijosa, Rodrigo Olea

Research output: Contribution to journalArticle

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.

Original languageEnglish
Article number221
JournalJournal of High Energy Physics
Volume2019
Issue number10
DOIs
Publication statusPublished - 1 Oct 2019

Fingerprint

entropy
gravitation
replicas
holography
compatibility
theorems

Keywords

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

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Cite this

Anastasiou, Giorgos ; Araya, Ignacio J. ; Güijosa, Alberto ; Olea, Rodrigo. / Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs. In: Journal of High Energy Physics. 2019 ; Vol. 2019, No. 10.
@article{877b5f8433c342c89ed55851fef7e894,
title = "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 gravity side, the computation considers extrin- sic counterterms and the use of the replica trick {\`a} 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",
author = "Giorgos Anastasiou and Araya, {Ignacio J.} and Alberto G{\"u}ijosa and Rodrigo Olea",
year = "2019",
month = "10",
day = "1",
doi = "10.1007/JHEP10(2019)221",
language = "English",
volume = "2019",
journal = "Journal of High Energy Physics",
issn = "1126-6708",
publisher = "Springer Verlag",
number = "10",

}

Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs. / Anastasiou, Giorgos; Araya, Ignacio J.; Güijosa, Alberto; Olea, Rodrigo.

In: Journal of High Energy Physics, Vol. 2019, No. 10, 221, 01.10.2019.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs

AU - Anastasiou, Giorgos

AU - Araya, Ignacio J.

AU - Güijosa, Alberto

AU - Olea, Rodrigo

PY - 2019/10/1

Y1 - 2019/10/1

N2 - 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.

AB - 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.

KW - AdS-CFT Correspondence

KW - Classical Theories of Gravity

KW - Gauge-gravity correspondence

UR - http://www.scopus.com/inward/record.url?scp=85074268519&partnerID=8YFLogxK

U2 - 10.1007/JHEP10(2019)221

DO - 10.1007/JHEP10(2019)221

M3 - Article

AN - SCOPUS:85074268519

VL - 2019

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 10

M1 - 221

ER -