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

N1 - Funding Information:
Article funded by SCOAP3.
Funding Information:
It is a pleasure to thank César Arias, Stefan Theisen and David Vergara for useful discussions. The work of GA, IJA and RO was funded in part by FONDECYT Grants No. 1170765 Boundary dynamics in anti-de Sitter gravity and gauge/gravity duality, No. 3180620 Entanglement Entropy and AdS gravity and No. 3190314 Holographic Complexity from anti-de Sitter gravity. The work of AG was partially supported by Mexico’s National Council of Science and Technology (CONACyT) grant A1-S-22886 and DGAPA-UNAM grant IN107520.

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 -