Positivity, entanglement entropy, and minimal surfaces

Autores
Casini, Horacio German; Huerta, Marina
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The path integral representation for the Renyi entanglement entropies of integer index n implies these information measures define operator correlation functions in QFT. We analyze whether the limit n → 1, corresponding to the entanglement entropy, can also be represented in terms of a path integral with insertions on the region's boundary, at first order in n-1. This conjecture has been used in the literature in several occasions, and specially in an attempt to prove the Ryu-Takayanagi holographic entanglement entropy formula. We show it leads to conditional positivity of the entropy correlation matrices, which is equivalent to an infinite series of polynomial inequalities for the entropies in QFT or the areas of minimal surfaces representing the entanglement entropy in the AdS-CFT context. We check these inequalities in several examples. No counterexample is found in the few known exact results for the entanglement entropy in QFT. The inequalities are also remarkable satisfied for several classes of minimal surfaces but we find counterexamples corresponding to more complicated geometries. We develop some analytic tools to test the inequalities, and as a byproduct, we show that positivity for the correlation functions is a local property when supplemented with analyticity. We also review general aspects of positivity for large N theories and Wilson loops in AdS-CFT.
Fil: Casini, Horacio German. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina
Fil: Huerta, Marina. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina
Materia
THOOFT AND POLYAKOV LOOPS
ADS-CFT CORRESPONDENCE
FIELD THEORIES IN HIGHER DIMENSIONS
FIELD THEORIES IN LOWER DIMENSIONS
WILSON
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:11336/198940
Acceder
id CONICETDig_16e65f45dfbf19125457dd2b43fe5059
oai_identifier_str oai:ri.conicet.gov.ar:11336/198940
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Positivity, entanglement entropy, and minimal surfacesCasini, Horacio GermanHuerta, MarinaTHOOFT AND POLYAKOV LOOPSADS-CFT CORRESPONDENCEFIELD THEORIES IN HIGHER DIMENSIONSFIELD THEORIES IN LOWER DIMENSIONSWILSONhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The path integral representation for the Renyi entanglement entropies of integer index n implies these information measures define operator correlation functions in QFT. We analyze whether the limit n → 1, corresponding to the entanglement entropy, can also be represented in terms of a path integral with insertions on the region's boundary, at first order in n-1. This conjecture has been used in the literature in several occasions, and specially in an attempt to prove the Ryu-Takayanagi holographic entanglement entropy formula. We show it leads to conditional positivity of the entropy correlation matrices, which is equivalent to an infinite series of polynomial inequalities for the entropies in QFT or the areas of minimal surfaces representing the entanglement entropy in the AdS-CFT context. We check these inequalities in several examples. No counterexample is found in the few known exact results for the entanglement entropy in QFT. The inequalities are also remarkable satisfied for several classes of minimal surfaces but we find counterexamples corresponding to more complicated geometries. We develop some analytic tools to test the inequalities, and as a byproduct, we show that positivity for the correlation functions is a local property when supplemented with analyticity. We also review general aspects of positivity for large N theories and Wilson loops in AdS-CFT.Fil: Casini, Horacio German. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; ArgentinaFil: Huerta, Marina. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; ArgentinaSpringer2012-11info: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/11336/198940Casini, Horacio German; Huerta, Marina; Positivity, entanglement entropy, and minimal surfaces; Springer; Journal of High Energy Physics; 2012; 11; 11-2012; 1-371126-6708CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/JHEP11(2012)087info:eu-repo/semantics/altIdentifier/doi/10.1007/JHEP11(2012)087info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-29T12:11:17Zoai:ri.conicet.gov.ar:11336/198940instacron: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:34982025-10-29 12:11:17.87CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Positivity, entanglement entropy, and minimal surfaces
title Positivity, entanglement entropy, and minimal surfaces
spellingShingle Positivity, entanglement entropy, and minimal surfaces
Casini, Horacio German
THOOFT AND POLYAKOV LOOPS
ADS-CFT CORRESPONDENCE
FIELD THEORIES IN HIGHER DIMENSIONS
FIELD THEORIES IN LOWER DIMENSIONS
WILSON
title_short Positivity, entanglement entropy, and minimal surfaces
title_full Positivity, entanglement entropy, and minimal surfaces
title_fullStr Positivity, entanglement entropy, and minimal surfaces
title_full_unstemmed Positivity, entanglement entropy, and minimal surfaces
title_sort Positivity, entanglement entropy, and minimal surfaces
dc.creator.none.fl_str_mv Casini, Horacio German
Huerta, Marina
author Casini, Horacio German
author_facet Casini, Horacio German
Huerta, Marina
author_role author
author2 Huerta, Marina
author2_role author
dc.subject.none.fl_str_mv THOOFT AND POLYAKOV LOOPS
ADS-CFT CORRESPONDENCE
FIELD THEORIES IN HIGHER DIMENSIONS
FIELD THEORIES IN LOWER DIMENSIONS
WILSON
topic THOOFT AND POLYAKOV LOOPS
ADS-CFT CORRESPONDENCE
FIELD THEORIES IN HIGHER DIMENSIONS
FIELD THEORIES IN LOWER DIMENSIONS
WILSON
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The path integral representation for the Renyi entanglement entropies of integer index n implies these information measures define operator correlation functions in QFT. We analyze whether the limit n → 1, corresponding to the entanglement entropy, can also be represented in terms of a path integral with insertions on the region's boundary, at first order in n-1. This conjecture has been used in the literature in several occasions, and specially in an attempt to prove the Ryu-Takayanagi holographic entanglement entropy formula. We show it leads to conditional positivity of the entropy correlation matrices, which is equivalent to an infinite series of polynomial inequalities for the entropies in QFT or the areas of minimal surfaces representing the entanglement entropy in the AdS-CFT context. We check these inequalities in several examples. No counterexample is found in the few known exact results for the entanglement entropy in QFT. The inequalities are also remarkable satisfied for several classes of minimal surfaces but we find counterexamples corresponding to more complicated geometries. We develop some analytic tools to test the inequalities, and as a byproduct, we show that positivity for the correlation functions is a local property when supplemented with analyticity. We also review general aspects of positivity for large N theories and Wilson loops in AdS-CFT.
Fil: Casini, Horacio German. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina
Fil: Huerta, Marina. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina
description The path integral representation for the Renyi entanglement entropies of integer index n implies these information measures define operator correlation functions in QFT. We analyze whether the limit n → 1, corresponding to the entanglement entropy, can also be represented in terms of a path integral with insertions on the region's boundary, at first order in n-1. This conjecture has been used in the literature in several occasions, and specially in an attempt to prove the Ryu-Takayanagi holographic entanglement entropy formula. We show it leads to conditional positivity of the entropy correlation matrices, which is equivalent to an infinite series of polynomial inequalities for the entropies in QFT or the areas of minimal surfaces representing the entanglement entropy in the AdS-CFT context. We check these inequalities in several examples. No counterexample is found in the few known exact results for the entanglement entropy in QFT. The inequalities are also remarkable satisfied for several classes of minimal surfaces but we find counterexamples corresponding to more complicated geometries. We develop some analytic tools to test the inequalities, and as a byproduct, we show that positivity for the correlation functions is a local property when supplemented with analyticity. We also review general aspects of positivity for large N theories and Wilson loops in AdS-CFT.
publishDate 2012
dc.date.none.fl_str_mv 2012-11
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/11336/198940
Casini, Horacio German; Huerta, Marina; Positivity, entanglement entropy, and minimal surfaces; Springer; Journal of High Energy Physics; 2012; 11; 11-2012; 1-37
1126-6708
CONICET Digital
CONICET
url http://hdl.handle.net/11336/198940
identifier_str_mv Casini, Horacio German; Huerta, Marina; Positivity, entanglement entropy, and minimal surfaces; Springer; Journal of High Energy Physics; 2012; 11; 11-2012; 1-37
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/url/https://link.springer.com/article/10.1007/JHEP11(2012)087
info:eu-repo/semantics/altIdentifier/doi/10.1007/JHEP11(2012)087
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 13.10058

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