Shape dependence of renormalized holographic entanglement entropy - Archive ouverte HAL
Article Dans Une Revue Journal of High Energy Physics Année : 2020

Shape dependence of renormalized holographic entanglement entropy

Giorgos Anastasiou
  • Fonction : Auteur
Javier Moreno
  • Fonction : Auteur
Rodrigo Olea
  • Fonction : Auteur

Résumé

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 AdS$_{4}$/CFT$_{3}$, 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.

Dates et versions

hal-02497835 , version 1 (03-03-2020)

Identifiants

Citer

Giorgos Anastasiou, Javier Moreno, Rodrigo Olea, David Rivera-Betancour. Shape dependence of renormalized holographic entanglement entropy. Journal of High Energy Physics, 2020, 09, pp.173. ⟨10.1007/JHEP09(2020)173⟩. ⟨hal-02497835⟩
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