Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs
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Fecha
2019-10
Profesor/a Guía
Facultad/escuela
Idioma
en
Título de la revista
ISSN de la revista
Título del volumen
Editor
Springer Verlag
Nombre de Curso
Licencia CC
Atribución 4.0 Internacional (CC BY 4.0)
Licencia CC
https://creativecommons.org/licenses/by/4.0/deed.es
Resumen
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. © 2019, The Author(s).
Notas
Indexación: Scopus
Palabras clave
AdS-CFT Correspondence, Classical Theories of Gravity, Gauge-gravity correspondence
Citación
Journal of High Energy PhysicsOpen AccessVolume 2019, Issue 101 October 2019 Article number 221
DOI
10.1007/JHEP10(2019)221