The g-theorem and quantum information theory

A bstract We study boundary renormalization group flows between boundary conformal field theories in 1 + 1 dimensions using methods of quantum information theory. We define an entropic g -function for theories with impurities in terms of the relative entanglement entropy, and we prove that this g -f...

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Bibliographic Details
Published in:The journal of high energy physics 2016-10, Vol.2016 (10), p.1-34, Article 140
Main Authors: Casini, Horacio, Landea, Ignacio Salazar, Torroba, Gonzalo
Format: Article
Language:English
Subjects:
Boundaries
Classical and Quantum Gravitation
Correlation
Degrees of freedom
Elementary Particles
Entropy
Field theory
High energy physics
Impurities
Mathematical analysis
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum phenomena
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Theory
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Summary:A bstract We study boundary renormalization group flows between boundary conformal field theories in 1 + 1 dimensions using methods of quantum information theory. We define an entropic g -function for theories with impurities in terms of the relative entanglement entropy, and we prove that this g -function decreases along boundary renormalization group flows. This entropic g -theorem is valid at zero temperature, and is independent from the g -theorem based on the thermal partition function. We also discuss the mutual information in boundary RG flows, and how it encodes the correlations between the impurity and bulk degrees of freedom. Our results provide a quantum-information understanding of (boundary) RG flow as increase of distinguishability between the UV fixed point and the theory along the RG flow.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP10(2016)140