We study the finite term of the holographic entanglement entropy of finite domains with smooth shapes and for four dimensional gravitational backgrounds. Analytic expressions depending on the unit vectors normal to the minimal area surface are obtained for both stationary and time dependent spacetimes. The special cases of AdS4, asymptotically AdS4 black holes, domain wall geometries and Vaidya-AdS backgrounds have been analysed explicitly. When the bulk spacetime is AdS4, the finite term is the Willmore energy of the minimal area surface viewed as a submanifold of the three dimensional flat Euclidean space. For the static spacetimes, some numerical checks involving spatial regions delimited by ellipses and non convex domains have been performed. In the case of AdS4, the infinite wedge has been also considered, recovering the known analytic formula for the coefficient of the logarithmic divergence.

On shape dependence of holographic entanglement entropy in AdS4/CFT3

Fonda, Piermarco;Tonni, Erik
2015

Abstract

We study the finite term of the holographic entanglement entropy of finite domains with smooth shapes and for four dimensional gravitational backgrounds. Analytic expressions depending on the unit vectors normal to the minimal area surface are obtained for both stationary and time dependent spacetimes. The special cases of AdS4, asymptotically AdS4 black holes, domain wall geometries and Vaidya-AdS backgrounds have been analysed explicitly. When the bulk spacetime is AdS4, the finite term is the Willmore energy of the minimal area surface viewed as a submanifold of the three dimensional flat Euclidean space. For the static spacetimes, some numerical checks involving spatial regions delimited by ellipses and non convex domains have been performed. In the case of AdS4, the infinite wedge has been also considered, recovering the known analytic formula for the coefficient of the logarithmic divergence.
JOURNAL OF HIGH ENERGY PHYSICS
2015
12
1
58
037
10.1007/JHEP12(2015)037
https://arxiv.org/abs/1507.08507
Fonda, Piermarco; Seminara, D.; Tonni, Erik
File in questo prodotto:
File Dimensione Formato  
JHEP12(2015)037.pdf

accesso aperto

Licenza: Creative commons
3.43 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/32565
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 18
  • ???jsp.display-item.citation.isi??? 24
social impact