Relative entropy in CFT

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Oct 2018Embargo end date: 01 Jan 2017 Italy English Publisher:Elsevier BVJournal:Advances in Mathematics, volume 337, pages 139-170 (issn: 0001-8708,

Copyright policy )Funded by:EC | QUEST

Authors: Longo, Roberto; Xu, Feng;

doi: 10.1016/j.aim.2018.08.015 , 10.48550/arxiv.1712.07283

arXiv: 1712.07283

handle: 2108/215391

Relative entropy in CFT

- Summary
- Subjects
- Metrics

Abstract

By using Araki's relative entropy, Lieb's convexity and the theory of singular integrals, we compute the mutual information associated with free fermions, and we deduce many results about entropies for chiral CFT's which are embedded into free fermions, and their extensions. Such relative entropies in CFT are here computed explicitly for the first time in a mathematical rigorous way. Our results agree with previous computations by physicists based on heuristic arguments; in addition we uncover a surprising connection with the theory of subfactors, in particular by showing that a certain duality, which is argued to be true on physical grounds, is in fact violated if the global dimension of the conformal net is greater than $1.$

31 pages

Country

Italy

Related Organizations

University of California, Riverside
United States
University of Rome Tor Vergata
Italy

Keywords

High Energy Physics - Theory, Measures of information, entropy, relative entropy, Mathematics - Operator Algebras, FOS: Physical sciences, Mathematical Physics (math-ph), CFT, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Settore MAT/05 - ANALISI MATEMATICA, Coding theorems (Shannon theory), High Energy Physics - Theory (hep-th), FOS: Mathematics, Operator Algebras (math.OA), Mathematical Physics

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	41
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Top 10%
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 10%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Top 10%