Shape dependence of renormalized holographic entanglement entropy
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Fecha
2020-09
Profesor/a Guía
Facultad/escuela
Idioma
en
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Título del volumen
Editor
Springer Science and Business Media Deutschland GmbH
Nombre de Curso
Licencia CC
Attribution 4.0 International (CC BY 4.0)
Licencia CC
https://creativecommons.org/licenses/by/4.0/
Resumen
We study the holographic entanglement entropy of deformed entangling regions in three-dimensional CFTs dual to Einstein-AdS gravity, using a renormalization scheme based on the addition of extrinsic counterterms. In this prescription, when even- dimensional manifolds are considered, the universal contribution to the entanglement entropy is identified as the renormalized volume of the Ryu-Takayanagi hypersurface, which is written as the sum of a topological and a curvature term. It is shown that the change in the renormalized entanglement entropy due to the deformation of the entangling surface is encoded purely in the curvature contribution. In turn, as the topological part is given by the Euler characteristic of the Ryu-Takayanagi surface, it remains shape independent. Exploiting the covariant character of the extrinsic counterterms, we apply the renormalization scheme for the case of deformed entangling regions in AdS4/CFT3, recovering the results found in the literature. Finally, we provide a derivation of the relation between renormalized entanglement entropy and Willmore energy. The presence of a lower bound of the latter makes manifest the relation between the AdS curvature of the Ryu-Takayanagi surface and the strong subadditivity property. © 2020, The Author(s).
Notas
Indexación: Scopus.
Palabras clave
AdS-CFT Correspondence, Gauge-gravity correspondence
Citación
Journal of High Energy PhysicsOpen AccessVolume 2020, Issue 91 September 2020 Article number 173
DOI
10.1007/JHEP09(2020)173