Renyi mutual information inequalities from Rindler positivity

Autores
Blanco, David Daniel; Lanosa, Leandro Federico; Leston, Mauricio; Pérez Nadal, Guillermo
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Rindler positivity is a property that holds in any relativistic Quantum Field Theory and implies an infinite set of inequalities involving the exponential of the Rényi mutual information In (Ai,A¯ j) between Ai and A¯ j, where Ai is a spacelike region in the right Rindler wedge and A¯ j is the wedge reflection of Aj. We explore these inequalities in order to get local inequalities for In (A,A¯) as a function of the distance between A and its mirror region A¯. We show that the assumption, based on the cluster property of the vacuum, that In goes to zero when the distance goes to infinity, implies the more stringent and simple condition that Fn≡ e(n−1)I n should be a completely monotonic function of the distance, meaning that all the even (odd) derivatives are non-negative (non-positive). In the case of a CFT, we show that conformal invariance implies stronger conditions, including a sort of monotonicity of the Rényi mutual information for pairs of balls. An application of these inequalities to obtain constraints for the OPE coefficients of the 4-point function of certain twist operators is also discussed.
Fil: Blanco, David Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Lanosa, Leandro Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Leston, Mauricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina
Fil: Pérez Nadal, Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina
Materia
CONFORMAL FIELD THEORY
FIELD THEORIES IN LOWER DIMENSIONS
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:11336/147562
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Renyi mutual information inequalities from Rindler positivityBlanco, David DanielLanosa, Leandro FedericoLeston, MauricioPérez Nadal, GuillermoCONFORMAL FIELD THEORYFIELD THEORIES IN LOWER DIMENSIONShttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1Rindler positivity is a property that holds in any relativistic Quantum Field Theory and implies an infinite set of inequalities involving the exponential of the Rényi mutual information In (Ai,A¯ j) between Ai and A¯ j, where Ai is a spacelike region in the right Rindler wedge and A¯ j is the wedge reflection of Aj. We explore these inequalities in order to get local inequalities for In (A,A¯) as a function of the distance between A and its mirror region A¯. We show that the assumption, based on the cluster property of the vacuum, that In goes to zero when the distance goes to infinity, implies the more stringent and simple condition that Fn≡ e(n−1)I n should be a completely monotonic function of the distance, meaning that all the even (odd) derivatives are non-negative (non-positive). In the case of a CFT, we show that conformal invariance implies stronger conditions, including a sort of monotonicity of the Rényi mutual information for pairs of balls. An application of these inequalities to obtain constraints for the OPE coefficients of the 4-point function of certain twist operators is also discussed.Fil: Blanco, David Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Lanosa, Leandro Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Leston, Mauricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; ArgentinaFil: Pérez Nadal, Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaSpringer2019-12-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/147562Blanco, David Daniel; Lanosa, Leandro Federico; Leston, Mauricio; Pérez Nadal, Guillermo; Renyi mutual information inequalities from Rindler positivity; Springer; Journal of High Energy Physics; 2019; 78; 10-12-2019; 1-171126-6708CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/JHEP12(2019)078info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2FJHEP12%282019%29078info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1909.03144info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:13:19Zoai:ri.conicet.gov.ar:11336/147562instacron: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:34982025-09-10 13:13:19.689CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Renyi mutual information inequalities from Rindler positivity
title Renyi mutual information inequalities from Rindler positivity
spellingShingle Renyi mutual information inequalities from Rindler positivity
Blanco, David Daniel
CONFORMAL FIELD THEORY
FIELD THEORIES IN LOWER DIMENSIONS
title_short Renyi mutual information inequalities from Rindler positivity
title_full Renyi mutual information inequalities from Rindler positivity
title_fullStr Renyi mutual information inequalities from Rindler positivity
title_full_unstemmed Renyi mutual information inequalities from Rindler positivity
title_sort Renyi mutual information inequalities from Rindler positivity
dc.creator.none.fl_str_mv Blanco, David Daniel
Lanosa, Leandro Federico
Leston, Mauricio
Pérez Nadal, Guillermo
author Blanco, David Daniel
author_facet Blanco, David Daniel
Lanosa, Leandro Federico
Leston, Mauricio
Pérez Nadal, Guillermo
author_role author
author2 Lanosa, Leandro Federico
Leston, Mauricio
Pérez Nadal, Guillermo
author2_role author
author
author
dc.subject.none.fl_str_mv CONFORMAL FIELD THEORY
FIELD THEORIES IN LOWER DIMENSIONS
topic CONFORMAL FIELD THEORY
FIELD THEORIES IN LOWER DIMENSIONS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Rindler positivity is a property that holds in any relativistic Quantum Field Theory and implies an infinite set of inequalities involving the exponential of the Rényi mutual information In (Ai,A¯ j) between Ai and A¯ j, where Ai is a spacelike region in the right Rindler wedge and A¯ j is the wedge reflection of Aj. We explore these inequalities in order to get local inequalities for In (A,A¯) as a function of the distance between A and its mirror region A¯. We show that the assumption, based on the cluster property of the vacuum, that In goes to zero when the distance goes to infinity, implies the more stringent and simple condition that Fn≡ e(n−1)I n should be a completely monotonic function of the distance, meaning that all the even (odd) derivatives are non-negative (non-positive). In the case of a CFT, we show that conformal invariance implies stronger conditions, including a sort of monotonicity of the Rényi mutual information for pairs of balls. An application of these inequalities to obtain constraints for the OPE coefficients of the 4-point function of certain twist operators is also discussed.
Fil: Blanco, David Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Lanosa, Leandro Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Leston, Mauricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina
Fil: Pérez Nadal, Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina
description Rindler positivity is a property that holds in any relativistic Quantum Field Theory and implies an infinite set of inequalities involving the exponential of the Rényi mutual information In (Ai,A¯ j) between Ai and A¯ j, where Ai is a spacelike region in the right Rindler wedge and A¯ j is the wedge reflection of Aj. We explore these inequalities in order to get local inequalities for In (A,A¯) as a function of the distance between A and its mirror region A¯. We show that the assumption, based on the cluster property of the vacuum, that In goes to zero when the distance goes to infinity, implies the more stringent and simple condition that Fn≡ e(n−1)I n should be a completely monotonic function of the distance, meaning that all the even (odd) derivatives are non-negative (non-positive). In the case of a CFT, we show that conformal invariance implies stronger conditions, including a sort of monotonicity of the Rényi mutual information for pairs of balls. An application of these inequalities to obtain constraints for the OPE coefficients of the 4-point function of certain twist operators is also discussed.
publishDate 2019
dc.date.none.fl_str_mv 2019-12-10
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/11336/147562
Blanco, David Daniel; Lanosa, Leandro Federico; Leston, Mauricio; Pérez Nadal, Guillermo; Renyi mutual information inequalities from Rindler positivity; Springer; Journal of High Energy Physics; 2019; 78; 10-12-2019; 1-17
1126-6708
CONICET Digital
CONICET
url http://hdl.handle.net/11336/147562
identifier_str_mv Blanco, David Daniel; Lanosa, Leandro Federico; Leston, Mauricio; Pérez Nadal, Guillermo; Renyi mutual information inequalities from Rindler positivity; Springer; Journal of High Energy Physics; 2019; 78; 10-12-2019; 1-17
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/JHEP12(2019)078
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2FJHEP12%282019%29078
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1909.03144
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
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 12.993085

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