Relative entropy and the RG flow

Autores
Casini, Horacio German; Testé Lino, Eduardo; Torroba, Gonzalo
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider the relative entropy between vacuum states of two different theories: a conformal field theory (CFT), and the CFT perturbed by a relevant operator. By restricting both states to the null Cauchy surface in the causal domain of a sphere, we make the relative entropy equal to the difference of entanglement entropies. As a result, this difference has the positivity and monotonicity properties of relative entropy. From this it follows a simple alternative proof of the c-theorem in d = 2 space-time dimensions and, for d > 2, the proof that the coefficient of the area term in the entanglement entropy decreases along the renormalization group (RG) flow between fixed points. We comment on the regimes of convergence of relative entropy, depending on the space-time dimensions and the conformal dimension Δ of the perturbation that triggers the RG flow.
Fil: Casini, Horacio German. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
Fil: Testé Lino, Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
Fil: Torroba, Gonzalo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
Materia
CONFORMAL FIELD THEORY
RENORMALIZATION GROUP
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/57963
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Relative entropy and the RG flowCasini, Horacio GermanTesté Lino, EduardoTorroba, GonzaloCONFORMAL FIELD THEORYRENORMALIZATION GROUPhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We consider the relative entropy between vacuum states of two different theories: a conformal field theory (CFT), and the CFT perturbed by a relevant operator. By restricting both states to the null Cauchy surface in the causal domain of a sphere, we make the relative entropy equal to the difference of entanglement entropies. As a result, this difference has the positivity and monotonicity properties of relative entropy. From this it follows a simple alternative proof of the c-theorem in d = 2 space-time dimensions and, for d > 2, the proof that the coefficient of the area term in the entanglement entropy decreases along the renormalization group (RG) flow between fixed points. We comment on the regimes of convergence of relative entropy, depending on the space-time dimensions and the conformal dimension Δ of the perturbation that triggers the RG flow.Fil: Casini, Horacio German. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaFil: Testé Lino, Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaFil: Torroba, Gonzalo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaSpringer2017-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/57963Casini, Horacio German; Testé Lino, Eduardo; Torroba, Gonzalo; Relative entropy and the RG flow; Springer; Journal of High Energy Physics; 2017; 3; 3-2017; 1-281126-6708CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/JHEP03(2017)089info:eu-repo/semantics/altIdentifier/url/ttps://link.springer.com/article/10.1007%2FJHEP03%282017%29089info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:36:26Zoai:ri.conicet.gov.ar:11336/57963instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:36:26.926CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Relative entropy and the RG flow
title Relative entropy and the RG flow
spellingShingle Relative entropy and the RG flow
Casini, Horacio German
CONFORMAL FIELD THEORY
RENORMALIZATION GROUP
title_short Relative entropy and the RG flow
title_full Relative entropy and the RG flow
title_fullStr Relative entropy and the RG flow
title_full_unstemmed Relative entropy and the RG flow
title_sort Relative entropy and the RG flow
dc.creator.none.fl_str_mv Casini, Horacio German
Testé Lino, Eduardo
Torroba, Gonzalo
author Casini, Horacio German
author_facet Casini, Horacio German
Testé Lino, Eduardo
Torroba, Gonzalo
author_role author
author2 Testé Lino, Eduardo
Torroba, Gonzalo
author2_role author
author
dc.subject.none.fl_str_mv CONFORMAL FIELD THEORY
RENORMALIZATION GROUP
topic CONFORMAL FIELD THEORY
RENORMALIZATION GROUP
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We consider the relative entropy between vacuum states of two different theories: a conformal field theory (CFT), and the CFT perturbed by a relevant operator. By restricting both states to the null Cauchy surface in the causal domain of a sphere, we make the relative entropy equal to the difference of entanglement entropies. As a result, this difference has the positivity and monotonicity properties of relative entropy. From this it follows a simple alternative proof of the c-theorem in d = 2 space-time dimensions and, for d > 2, the proof that the coefficient of the area term in the entanglement entropy decreases along the renormalization group (RG) flow between fixed points. We comment on the regimes of convergence of relative entropy, depending on the space-time dimensions and the conformal dimension Δ of the perturbation that triggers the RG flow.
Fil: Casini, Horacio German. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
Fil: Testé Lino, Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
Fil: Torroba, Gonzalo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
description We consider the relative entropy between vacuum states of two different theories: a conformal field theory (CFT), and the CFT perturbed by a relevant operator. By restricting both states to the null Cauchy surface in the causal domain of a sphere, we make the relative entropy equal to the difference of entanglement entropies. As a result, this difference has the positivity and monotonicity properties of relative entropy. From this it follows a simple alternative proof of the c-theorem in d = 2 space-time dimensions and, for d > 2, the proof that the coefficient of the area term in the entanglement entropy decreases along the renormalization group (RG) flow between fixed points. We comment on the regimes of convergence of relative entropy, depending on the space-time dimensions and the conformal dimension Δ of the perturbation that triggers the RG flow.
publishDate 2017
dc.date.none.fl_str_mv 2017-03
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/57963
Casini, Horacio German; Testé Lino, Eduardo; Torroba, Gonzalo; Relative entropy and the RG flow; Springer; Journal of High Energy Physics; 2017; 3; 3-2017; 1-28
1126-6708
CONICET Digital
CONICET
url http://hdl.handle.net/11336/57963
identifier_str_mv Casini, Horacio German; Testé Lino, Eduardo; Torroba, Gonzalo; Relative entropy and the RG flow; Springer; Journal of High Energy Physics; 2017; 3; 3-2017; 1-28
1126-6708
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/JHEP03(2017)089
info:eu-repo/semantics/altIdentifier/url/ttps://link.springer.com/article/10.1007%2FJHEP03%282017%29089
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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