### Abstract

We exhibit the equivalence between the renormalized volume of asymptotically anti-de Sitter (AAdS) Einstein manifolds in four and six dimensions, and their renormalized Euclidean bulk gravity actions. The action is that of Einstein gravity, where the renormalization is achieved through the addition of a single topological term. We generalize this equivalence, proposing an explicit form for the renormalized volume of higher even-dimensional AAdS Einstein manifolds. We also show that evaluating the renormalized bulk gravity action on the conically singular manifold of the replica trick results in an action principle that corresponds to the renormalized volume of the regular part of the bulk, plus the renormalized area of a codimension-2 cosmic brane whose tension is related to the replica index. Renormalized Rényi entropy of odd-dimensional holographic CFTs can thus be obtained from the renormalized area of the brane with finite tension, including the effects of its backreaction on the bulk geometry. The area computation corresponds to an extremization problem for an enclosing surface that extends to the AdS boundary, where the newly defined renormalized volume is considered.

Original language | English |
---|---|

Article number | 136 |

Journal | Journal of High Energy Physics |

Volume | 2018 |

Issue number | 8 |

DOIs | |

Publication status | Published - 1 Aug 2018 |

### Fingerprint

### Keywords

- AdS-CFT Correspondence
- Classical Theories of Gravity
- Gauge-gravity correspondence

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2018*(8), [136]. https://doi.org/10.1007/JHEP08(2018)136

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*Journal of High Energy Physics*, vol. 2018, no. 8, 136. https://doi.org/10.1007/JHEP08(2018)136

**Einstein-AdS action, renormalized volume/area and holographic Rényi entropies.** / Anastasiou, Giorgos; Araya, Ignacio J.; Arias, Cesar; Olea, Rodrigo.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Einstein-AdS action, renormalized volume/area and holographic Rényi entropies

AU - Anastasiou, Giorgos

AU - Araya, Ignacio J.

AU - Arias, Cesar

AU - Olea, Rodrigo

PY - 2018/8/1

Y1 - 2018/8/1

N2 - We exhibit the equivalence between the renormalized volume of asymptotically anti-de Sitter (AAdS) Einstein manifolds in four and six dimensions, and their renormalized Euclidean bulk gravity actions. The action is that of Einstein gravity, where the renormalization is achieved through the addition of a single topological term. We generalize this equivalence, proposing an explicit form for the renormalized volume of higher even-dimensional AAdS Einstein manifolds. We also show that evaluating the renormalized bulk gravity action on the conically singular manifold of the replica trick results in an action principle that corresponds to the renormalized volume of the regular part of the bulk, plus the renormalized area of a codimension-2 cosmic brane whose tension is related to the replica index. Renormalized Rényi entropy of odd-dimensional holographic CFTs can thus be obtained from the renormalized area of the brane with finite tension, including the effects of its backreaction on the bulk geometry. The area computation corresponds to an extremization problem for an enclosing surface that extends to the AdS boundary, where the newly defined renormalized volume is considered.

AB - We exhibit the equivalence between the renormalized volume of asymptotically anti-de Sitter (AAdS) Einstein manifolds in four and six dimensions, and their renormalized Euclidean bulk gravity actions. The action is that of Einstein gravity, where the renormalization is achieved through the addition of a single topological term. We generalize this equivalence, proposing an explicit form for the renormalized volume of higher even-dimensional AAdS Einstein manifolds. We also show that evaluating the renormalized bulk gravity action on the conically singular manifold of the replica trick results in an action principle that corresponds to the renormalized volume of the regular part of the bulk, plus the renormalized area of a codimension-2 cosmic brane whose tension is related to the replica index. Renormalized Rényi entropy of odd-dimensional holographic CFTs can thus be obtained from the renormalized area of the brane with finite tension, including the effects of its backreaction on the bulk geometry. The area computation corresponds to an extremization problem for an enclosing surface that extends to the AdS boundary, where the newly defined renormalized volume is considered.

KW - AdS-CFT Correspondence

KW - Classical Theories of Gravity

KW - Gauge-gravity correspondence

UR - http://www.scopus.com/inward/record.url?scp=85052118531&partnerID=8YFLogxK

U2 - 10.1007/JHEP08(2018)136

DO - 10.1007/JHEP08(2018)136

M3 - Article

AN - SCOPUS:85052118531

VL - 2018

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 8

M1 - 136

ER -