### Resumen

We extend our topological renormalization scheme for entanglement entropy to holographic CFTs of arbitrary odd dimensions in the context of the AdS/CFT correspondence. The procedure consists in adding the Chern form as a boundary term to the area functional of the Ryu-Takayanagi minimal surface. The renormalized entanglement entropy thus obtained can be rewritten in terms of the Euler characteristic and the AdS curvature of the minimal surface. This prescription considers the use of the replica trick to express the renormalized entanglement entropy in terms of the renormalized gravitational action evaluated on the conically singular replica manifold extended to the bulk. This renormalized action is obtained in turn by adding the Chern form as the counterterm at the boundary of the 2n-dimensional asymptotically AdS bulk manifold. We explicitly show that, up to next-to-leading order in the holographic radial coordinate, the addition of this boundary term cancels the divergent part of the entanglement entropy. We discuss possible applications of the method for studying CFT parameters like central charges.

Idioma original | English |
---|---|

Número de artículo | 106015 |

Publicación | Physical Review D |

Volumen | 97 |

N.º | 10 |

DOI | |

Estado | Published - 15 may 2018 |

### Huella dactilar

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Citar esto

*Physical Review D*,

*97*(10), [106015]. https://doi.org/10.1103/PhysRevD.97.106015

}

*Physical Review D*, vol. 97, n.º 10, 106015. https://doi.org/10.1103/PhysRevD.97.106015

**Topological terms, AdS2n gravity, and renormalized entanglement entropy of holographic CFTs.** / Anastasiou, Giorgos; Araya, Ignacio J.; Olea, Rodrigo.

Resultado de la investigación: Article

TY - JOUR

T1 - Topological terms, AdS2n gravity, and renormalized entanglement entropy of holographic CFTs

AU - Anastasiou, Giorgos

AU - Araya, Ignacio J.

AU - Olea, Rodrigo

PY - 2018/5/15

Y1 - 2018/5/15

N2 - We extend our topological renormalization scheme for entanglement entropy to holographic CFTs of arbitrary odd dimensions in the context of the AdS/CFT correspondence. The procedure consists in adding the Chern form as a boundary term to the area functional of the Ryu-Takayanagi minimal surface. The renormalized entanglement entropy thus obtained can be rewritten in terms of the Euler characteristic and the AdS curvature of the minimal surface. This prescription considers the use of the replica trick to express the renormalized entanglement entropy in terms of the renormalized gravitational action evaluated on the conically singular replica manifold extended to the bulk. This renormalized action is obtained in turn by adding the Chern form as the counterterm at the boundary of the 2n-dimensional asymptotically AdS bulk manifold. We explicitly show that, up to next-to-leading order in the holographic radial coordinate, the addition of this boundary term cancels the divergent part of the entanglement entropy. We discuss possible applications of the method for studying CFT parameters like central charges.

AB - We extend our topological renormalization scheme for entanglement entropy to holographic CFTs of arbitrary odd dimensions in the context of the AdS/CFT correspondence. The procedure consists in adding the Chern form as a boundary term to the area functional of the Ryu-Takayanagi minimal surface. The renormalized entanglement entropy thus obtained can be rewritten in terms of the Euler characteristic and the AdS curvature of the minimal surface. This prescription considers the use of the replica trick to express the renormalized entanglement entropy in terms of the renormalized gravitational action evaluated on the conically singular replica manifold extended to the bulk. This renormalized action is obtained in turn by adding the Chern form as the counterterm at the boundary of the 2n-dimensional asymptotically AdS bulk manifold. We explicitly show that, up to next-to-leading order in the holographic radial coordinate, the addition of this boundary term cancels the divergent part of the entanglement entropy. We discuss possible applications of the method for studying CFT parameters like central charges.

UR - http://www.scopus.com/inward/record.url?scp=85048075816&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.97.106015

DO - 10.1103/PhysRevD.97.106015

M3 - Article

VL - 97

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 10

M1 - 106015

ER -