Entanglement Rényi entropies in conformal field theories and holography

A bstract An entanglement Rényi entropy for a spatial partition of a system is studied in conformal theories which admit a dual description in terms of an anti-de Sitter gravity. The divergent part of the Rényi entropy is computed in 4D conformal super Yang- Mills theory at a weak coupling. This res...

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Bibliographic Details
Published in:The journal of high energy physics 2012-05, Vol.2012 (5), Article 80
Main Author: Fursaev, D. V.
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Elementary Particles
Entanglement
Entropy
High energy physics
Holography
Hyperspaces
Physics
Physics and Astronomy
Polynomials
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Relativity Theory
String Theory
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Summary:A bstract An entanglement Rényi entropy for a spatial partition of a system is studied in conformal theories which admit a dual description in terms of an anti-de Sitter gravity. The divergent part of the Rényi entropy is computed in 4D conformal super Yang- Mills theory at a weak coupling. This result is used to suggest a holographic formula which reproduces the Rényi entropy at least in the leading approximation. The holographic Rényi entropy is an invariant functional set on a codimension 2 minimal hypersurface in the bulk geometry. The bulk space does not depend on order n of the Rényi entropy. The holographic Rényi entropy is a sum of local and non-local functionals multiplied by polynomials of 1/ n .
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP05(2012)080