Reflected entropy for free scalars

Autores
Bueno, Pablo; Casini, Horacio German
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We continue our study of reflected entropy, R(A, B), for Gaussian systems. In this paper we provide general formulas valid for free scalar fields in arbitrary dimensions. Similarly to the fermionic case, the resulting expressions are fully determined in terms of correlators of the fields, making them amenable to lattice calculations. We apply this to the case of a (1 + 1)-dimensional chiral scalar, whose reflected entropy we compute for two intervals as a function of the cross-ratio, comparing it with previous holographic and free-fermion results. For both types of free theories we find that reflected entropy satisfies the conjectural monotonicity property R(A, BC) ≥ R(A, B). Then, we move to (2 + 1) dimensions and evaluate it for square regions for free scalars, fermions and holography, determining the very-far and very-close regimes and comparing them with their mutual information counterparts. In all cases considered, both for (1 + 1)- and (2 + 1)-dimensional theories, we verify that the general inequality relating both quantities, R(A, B) ≥ I (A, B), is satisfied. Our results suggest that for general regions characterized by length-scales LA ∼ LB ∼ L and separated a distance ℓ, the reflected entropy in the large-separation regime (x ≡ L/ℓ ≪ 1) behaves as R(x) ∼ −I(x) log x for general CFTs in arbitrary dimensions.
Fil: Bueno, Pablo. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina
Fil: Casini, Horacio German. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina
Materia
ADS-CFT CORRESPONDENCE
CONFORMAL FIELD THEORY
FIELD THEORIES IN LOWER DIMENSIONS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/150182
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Reflected entropy for free scalarsBueno, PabloCasini, Horacio GermanADS-CFT CORRESPONDENCECONFORMAL FIELD THEORYFIELD THEORIES IN LOWER DIMENSIONShttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We continue our study of reflected entropy, R(A, B), for Gaussian systems. In this paper we provide general formulas valid for free scalar fields in arbitrary dimensions. Similarly to the fermionic case, the resulting expressions are fully determined in terms of correlators of the fields, making them amenable to lattice calculations. We apply this to the case of a (1 + 1)-dimensional chiral scalar, whose reflected entropy we compute for two intervals as a function of the cross-ratio, comparing it with previous holographic and free-fermion results. For both types of free theories we find that reflected entropy satisfies the conjectural monotonicity property R(A, BC) ≥ R(A, B). Then, we move to (2 + 1) dimensions and evaluate it for square regions for free scalars, fermions and holography, determining the very-far and very-close regimes and comparing them with their mutual information counterparts. In all cases considered, both for (1 + 1)- and (2 + 1)-dimensional theories, we verify that the general inequality relating both quantities, R(A, B) ≥ I (A, B), is satisfied. Our results suggest that for general regions characterized by length-scales LA ∼ LB ∼ L and separated a distance ℓ, the reflected entropy in the large-separation regime (x ≡ L/ℓ ≪ 1) behaves as R(x) ∼ −I(x) log x for general CFTs in arbitrary dimensions.Fil: Bueno, Pablo. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; ArgentinaFil: Casini, Horacio German. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; ArgentinaSpringer2020-11info: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/11336/150182Bueno, Pablo; Casini, Horacio German; Reflected entropy for free scalars; Springer; Journal of High Energy Physics; 2020; 11; 11-2020; 1-281029-8479CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/JHEP11(2020)148info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2FJHEP11%282020%29148info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:09:19Zoai:ri.conicet.gov.ar:11336/150182instacron: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 13:09:19.62CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Reflected entropy for free scalars
title Reflected entropy for free scalars
spellingShingle Reflected entropy for free scalars
Bueno, Pablo
ADS-CFT CORRESPONDENCE
CONFORMAL FIELD THEORY
FIELD THEORIES IN LOWER DIMENSIONS
title_short Reflected entropy for free scalars
title_full Reflected entropy for free scalars
title_fullStr Reflected entropy for free scalars
title_full_unstemmed Reflected entropy for free scalars
title_sort Reflected entropy for free scalars
dc.creator.none.fl_str_mv Bueno, Pablo
Casini, Horacio German
author Bueno, Pablo
author_facet Bueno, Pablo
Casini, Horacio German
author_role author
author2 Casini, Horacio German
author2_role author
dc.subject.none.fl_str_mv ADS-CFT CORRESPONDENCE
CONFORMAL FIELD THEORY
FIELD THEORIES IN LOWER DIMENSIONS
topic ADS-CFT CORRESPONDENCE
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
dc.description.none.fl_txt_mv We continue our study of reflected entropy, R(A, B), for Gaussian systems. In this paper we provide general formulas valid for free scalar fields in arbitrary dimensions. Similarly to the fermionic case, the resulting expressions are fully determined in terms of correlators of the fields, making them amenable to lattice calculations. We apply this to the case of a (1 + 1)-dimensional chiral scalar, whose reflected entropy we compute for two intervals as a function of the cross-ratio, comparing it with previous holographic and free-fermion results. For both types of free theories we find that reflected entropy satisfies the conjectural monotonicity property R(A, BC) ≥ R(A, B). Then, we move to (2 + 1) dimensions and evaluate it for square regions for free scalars, fermions and holography, determining the very-far and very-close regimes and comparing them with their mutual information counterparts. In all cases considered, both for (1 + 1)- and (2 + 1)-dimensional theories, we verify that the general inequality relating both quantities, R(A, B) ≥ I (A, B), is satisfied. Our results suggest that for general regions characterized by length-scales LA ∼ LB ∼ L and separated a distance ℓ, the reflected entropy in the large-separation regime (x ≡ L/ℓ ≪ 1) behaves as R(x) ∼ −I(x) log x for general CFTs in arbitrary dimensions.
Fil: Bueno, Pablo. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina
Fil: Casini, Horacio German. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina
description We continue our study of reflected entropy, R(A, B), for Gaussian systems. In this paper we provide general formulas valid for free scalar fields in arbitrary dimensions. Similarly to the fermionic case, the resulting expressions are fully determined in terms of correlators of the fields, making them amenable to lattice calculations. We apply this to the case of a (1 + 1)-dimensional chiral scalar, whose reflected entropy we compute for two intervals as a function of the cross-ratio, comparing it with previous holographic and free-fermion results. For both types of free theories we find that reflected entropy satisfies the conjectural monotonicity property R(A, BC) ≥ R(A, B). Then, we move to (2 + 1) dimensions and evaluate it for square regions for free scalars, fermions and holography, determining the very-far and very-close regimes and comparing them with their mutual information counterparts. In all cases considered, both for (1 + 1)- and (2 + 1)-dimensional theories, we verify that the general inequality relating both quantities, R(A, B) ≥ I (A, B), is satisfied. Our results suggest that for general regions characterized by length-scales LA ∼ LB ∼ L and separated a distance ℓ, the reflected entropy in the large-separation regime (x ≡ L/ℓ ≪ 1) behaves as R(x) ∼ −I(x) log x for general CFTs in arbitrary dimensions.
publishDate 2020
dc.date.none.fl_str_mv 2020-11
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/11336/150182
Bueno, Pablo; Casini, Horacio German; Reflected entropy for free scalars; Springer; Journal of High Energy Physics; 2020; 11; 11-2020; 1-28
1029-8479
CONICET Digital
CONICET
url http://hdl.handle.net/11336/150182
identifier_str_mv Bueno, Pablo; Casini, Horacio German; Reflected entropy for free scalars; Springer; Journal of High Energy Physics; 2020; 11; 11-2020; 1-28
1029-8479
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/JHEP11(2020)148
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2FJHEP11%282020%29148
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/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 12.993085

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