ABJ anomaly as a U(1) symmetry and Noether's theorem

Autores
Benedetti, Valentin; Casini, Horacio German; Magán, Javier M.
Año de publicación
2023
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The Adler-Bell-Jackiw anomaly determines the violation of chiral symmetry when massless fermions are coupled to an abelian gauge field. In its seminal paper, Adler noticed that a modified chiral U(1) symmetry could still be defined, at the expense of being generated by a non-gauge-invariant conserved current. We show this internal U(1) symmetry has the special feature that it transforms the Haag duality violating sectors (or non local operator classes). This provides a simple unifying perspective on the origin of anomaly quantization, anomaly matching, applicability of Goldstone theorem, and the absence of a Noether current. We comment on recent literature where this symmetry is considered to be either absent or non-invertible. We end by recalling the DHR reconstruction theorem, which states 0-form symmetries cannot be non-invertible for d>2, and argue for a higher form-symmetry reconstruction theorem.
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: Magán, Javier M.. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
Materia
ABJ ANOMALY
GENERALIZED SYMMETRIES
NOETHER CURRENT
NON-INVERTIBLE SYMMETRIES
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:11336/247950
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling ABJ anomaly as a U(1) symmetry and Noether's theoremBenedetti, ValentinCasini, Horacio GermanMagán, Javier M.ABJ ANOMALYGENERALIZED SYMMETRIESNOETHER CURRENTNON-INVERTIBLE SYMMETRIEShttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The Adler-Bell-Jackiw anomaly determines the violation of chiral symmetry when massless fermions are coupled to an abelian gauge field. In its seminal paper, Adler noticed that a modified chiral U(1) symmetry could still be defined, at the expense of being generated by a non-gauge-invariant conserved current. We show this internal U(1) symmetry has the special feature that it transforms the Haag duality violating sectors (or non local operator classes). This provides a simple unifying perspective on the origin of anomaly quantization, anomaly matching, applicability of Goldstone theorem, and the absence of a Noether current. We comment on recent literature where this symmetry is considered to be either absent or non-invertible. We end by recalling the DHR reconstruction theorem, which states 0-form symmetries cannot be non-invertible for d>2, and argue for a higher form-symmetry reconstruction theorem.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: Magán, Javier M.. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaCornell University2023-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/247950Benedetti, Valentin; Casini, Horacio German; Magán, Javier M.; ABJ anomaly as a U(1) symmetry and Noether's theorem; Cornell University; ArXiv; 2023; 9-2023; 1-482331-8422CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2309.03264info:eu-repo/semantics/altIdentifier/doi/10.48550/arXiv.2309.03264info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:55:59Zoai:ri.conicet.gov.ar:11336/247950instacron: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:34982025-10-22 11:56:00.042CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv ABJ anomaly as a U(1) symmetry and Noether's theorem
title ABJ anomaly as a U(1) symmetry and Noether's theorem
spellingShingle ABJ anomaly as a U(1) symmetry and Noether's theorem
Benedetti, Valentin
ABJ ANOMALY
GENERALIZED SYMMETRIES
NOETHER CURRENT
NON-INVERTIBLE SYMMETRIES
title_short ABJ anomaly as a U(1) symmetry and Noether's theorem
title_full ABJ anomaly as a U(1) symmetry and Noether's theorem
title_fullStr ABJ anomaly as a U(1) symmetry and Noether's theorem
title_full_unstemmed ABJ anomaly as a U(1) symmetry and Noether's theorem
title_sort ABJ anomaly as a U(1) symmetry and Noether's theorem
dc.creator.none.fl_str_mv Benedetti, Valentin
Casini, Horacio German
Magán, Javier M.
author Benedetti, Valentin
author_facet Benedetti, Valentin
Casini, Horacio German
Magán, Javier M.
author_role author
author2 Casini, Horacio German
Magán, Javier M.
author2_role author
author
dc.subject.none.fl_str_mv ABJ ANOMALY
GENERALIZED SYMMETRIES
NOETHER CURRENT
NON-INVERTIBLE SYMMETRIES
topic ABJ ANOMALY
GENERALIZED SYMMETRIES
NOETHER CURRENT
NON-INVERTIBLE SYMMETRIES
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 Adler-Bell-Jackiw anomaly determines the violation of chiral symmetry when massless fermions are coupled to an abelian gauge field. In its seminal paper, Adler noticed that a modified chiral U(1) symmetry could still be defined, at the expense of being generated by a non-gauge-invariant conserved current. We show this internal U(1) symmetry has the special feature that it transforms the Haag duality violating sectors (or non local operator classes). This provides a simple unifying perspective on the origin of anomaly quantization, anomaly matching, applicability of Goldstone theorem, and the absence of a Noether current. We comment on recent literature where this symmetry is considered to be either absent or non-invertible. We end by recalling the DHR reconstruction theorem, which states 0-form symmetries cannot be non-invertible for d>2, and argue for a higher form-symmetry reconstruction theorem.
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: Magán, Javier M.. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
description The Adler-Bell-Jackiw anomaly determines the violation of chiral symmetry when massless fermions are coupled to an abelian gauge field. In its seminal paper, Adler noticed that a modified chiral U(1) symmetry could still be defined, at the expense of being generated by a non-gauge-invariant conserved current. We show this internal U(1) symmetry has the special feature that it transforms the Haag duality violating sectors (or non local operator classes). This provides a simple unifying perspective on the origin of anomaly quantization, anomaly matching, applicability of Goldstone theorem, and the absence of a Noether current. We comment on recent literature where this symmetry is considered to be either absent or non-invertible. We end by recalling the DHR reconstruction theorem, which states 0-form symmetries cannot be non-invertible for d>2, and argue for a higher form-symmetry reconstruction theorem.
publishDate 2023
dc.date.none.fl_str_mv 2023-09
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/11336/247950
Benedetti, Valentin; Casini, Horacio German; Magán, Javier M.; ABJ anomaly as a U(1) symmetry and Noether's theorem; Cornell University; ArXiv; 2023; 9-2023; 1-48
2331-8422
CONICET Digital
CONICET
url http://hdl.handle.net/11336/247950
identifier_str_mv Benedetti, Valentin; Casini, Horacio German; Magán, Javier M.; ABJ anomaly as a U(1) symmetry and Noether's theorem; Cornell University; ArXiv; 2023; 9-2023; 1-48
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/2309.03264
info:eu-repo/semantics/altIdentifier/doi/10.48550/arXiv.2309.03264
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 12.982451

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