Modular invariance as completeness

Autores
Benedetti, Valentin; Casini, Horacio German; Kawahigashi, Yasuyuki; Longo, Roberto; Magán, Javier M.
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We review the physical meaning of modular invariance for unitary conformal quantum f ield theories in d = 2. For QFT models, while T invariance is necessary for locality, S invariance is not mandatory. S invariance is a form of completeness of the theory that has a precise meaning as Haag duality for arbitrary multi-interval regions. We present a mathematical proof as well as derive this result from a physical standpoint using Renyi entropies and the replica trick. For rational CFT’s, the failure of modular invariance or Haag duality can be measured by an index, related to the quantum dimensions of the model. We show how to compute this index from the modular transformation matrices. The index also appears in a limit of the Renyi mutual informations. Cases of infinite index are briefly discussed. Part of the argument can be extended to higher dimensions, where the lack of completeness can also be diagnosed using the CFT data through the thermal partition function and measured by an index.
Fil: Benedetti, Valentin. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; 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
Fil: Kawahigashi, Yasuyuki. University of Tokyo; Japón
Fil: Longo, Roberto. Universita Tor Vergata; Italia
Fil: Magán, Javier M.. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
Materia
MODULAR INVARIANCE
HAAG DUALITY
COMPLETENESS
CFT
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:11336/247877
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Modular invariance as completenessBenedetti, ValentinCasini, Horacio GermanKawahigashi, YasuyukiLongo, RobertoMagán, Javier M.MODULAR INVARIANCEHAAG DUALITYCOMPLETENESSCFThttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We review the physical meaning of modular invariance for unitary conformal quantum f ield theories in d = 2. For QFT models, while T invariance is necessary for locality, S invariance is not mandatory. S invariance is a form of completeness of the theory that has a precise meaning as Haag duality for arbitrary multi-interval regions. We present a mathematical proof as well as derive this result from a physical standpoint using Renyi entropies and the replica trick. For rational CFT’s, the failure of modular invariance or Haag duality can be measured by an index, related to the quantum dimensions of the model. We show how to compute this index from the modular transformation matrices. The index also appears in a limit of the Renyi mutual informations. Cases of infinite index are briefly discussed. Part of the argument can be extended to higher dimensions, where the lack of completeness can also be diagnosed using the CFT data through the thermal partition function and measured by an index.Fil: Benedetti, Valentin. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; 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; ArgentinaFil: Kawahigashi, Yasuyuki. University of Tokyo; JapónFil: Longo, Roberto. Universita Tor Vergata; ItaliaFil: Magán, Javier M.. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaCornell University2024-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/247877Benedetti, Valentin; Casini, Horacio German; Kawahigashi, Yasuyuki; Longo, Roberto; Magán, Javier M.; Modular invariance as completeness; Cornell University; ArXiv; 2024; 8-2024; 1-372331-84222331-8422CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2408.04011info:eu-repo/semantics/altIdentifier/doi/10.48550/arXiv.2408.04011info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-17T11:24:30Zoai:ri.conicet.gov.ar:11336/247877instacron: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:34982025-09-17 11:24:30.682CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Modular invariance as completeness
title Modular invariance as completeness
spellingShingle Modular invariance as completeness
Benedetti, Valentin
MODULAR INVARIANCE
HAAG DUALITY
COMPLETENESS
CFT
title_short Modular invariance as completeness
title_full Modular invariance as completeness
title_fullStr Modular invariance as completeness
title_full_unstemmed Modular invariance as completeness
title_sort Modular invariance as completeness
dc.creator.none.fl_str_mv Benedetti, Valentin
Casini, Horacio German
Kawahigashi, Yasuyuki
Longo, Roberto
Magán, Javier M.
author Benedetti, Valentin
author_facet Benedetti, Valentin
Casini, Horacio German
Kawahigashi, Yasuyuki
Longo, Roberto
Magán, Javier M.
author_role author
author2 Casini, Horacio German
Kawahigashi, Yasuyuki
Longo, Roberto
Magán, Javier M.
author2_role author
author
author
author
dc.subject.none.fl_str_mv MODULAR INVARIANCE
HAAG DUALITY
COMPLETENESS
CFT
topic MODULAR INVARIANCE
HAAG DUALITY
COMPLETENESS
CFT
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 review the physical meaning of modular invariance for unitary conformal quantum f ield theories in d = 2. For QFT models, while T invariance is necessary for locality, S invariance is not mandatory. S invariance is a form of completeness of the theory that has a precise meaning as Haag duality for arbitrary multi-interval regions. We present a mathematical proof as well as derive this result from a physical standpoint using Renyi entropies and the replica trick. For rational CFT’s, the failure of modular invariance or Haag duality can be measured by an index, related to the quantum dimensions of the model. We show how to compute this index from the modular transformation matrices. The index also appears in a limit of the Renyi mutual informations. Cases of infinite index are briefly discussed. Part of the argument can be extended to higher dimensions, where the lack of completeness can also be diagnosed using the CFT data through the thermal partition function and measured by an index.
Fil: Benedetti, Valentin. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; 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
Fil: Kawahigashi, Yasuyuki. University of Tokyo; Japón
Fil: Longo, Roberto. Universita Tor Vergata; Italia
Fil: Magán, Javier M.. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
description We review the physical meaning of modular invariance for unitary conformal quantum f ield theories in d = 2. For QFT models, while T invariance is necessary for locality, S invariance is not mandatory. S invariance is a form of completeness of the theory that has a precise meaning as Haag duality for arbitrary multi-interval regions. We present a mathematical proof as well as derive this result from a physical standpoint using Renyi entropies and the replica trick. For rational CFT’s, the failure of modular invariance or Haag duality can be measured by an index, related to the quantum dimensions of the model. We show how to compute this index from the modular transformation matrices. The index also appears in a limit of the Renyi mutual informations. Cases of infinite index are briefly discussed. Part of the argument can be extended to higher dimensions, where the lack of completeness can also be diagnosed using the CFT data through the thermal partition function and measured by an index.
publishDate 2024
dc.date.none.fl_str_mv 2024-08
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/11336/247877
Benedetti, Valentin; Casini, Horacio German; Kawahigashi, Yasuyuki; Longo, Roberto; Magán, Javier M.; Modular invariance as completeness; Cornell University; ArXiv; 2024; 8-2024; 1-37
2331-8422
2331-8422
CONICET Digital
CONICET
url http://hdl.handle.net/11336/247877
identifier_str_mv Benedetti, Valentin; Casini, Horacio German; Kawahigashi, Yasuyuki; Longo, Roberto; Magán, Javier M.; Modular invariance as completeness; Cornell University; ArXiv; 2024; 8-2024; 1-37
2331-8422
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://arxiv.org/abs/2408.04011
info:eu-repo/semantics/altIdentifier/doi/10.48550/arXiv.2408.04011
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 Cornell University
publisher.none.fl_str_mv Cornell University
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 13.001348

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