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

Giorgos Anastasiou, Ignacio J. Araya, Cesar Arias, Rodrigo Olea

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 languageEnglish
Article number136
JournalJournal of High Energy Physics
Volume2018
Issue number8
DOIs
Publication statusPublished - 1 Aug 2018

Keywords

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

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Fingerprint Dive into the research topics of 'Einstein-AdS action, renormalized volume/area and holographic Rényi entropies'. Together they form a unique fingerprint.

  • Cite this