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dc.contributor.author
Benedetti, Valentin
dc.contributor.author
Casini, Horacio German
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Kawahigashi, Yasuyuki
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Longo, Roberto
dc.contributor.author
Magán, Javier M.
dc.date.available
2024-11-11T15:57:10Z
dc.date.issued
2024-08
dc.identifier.citation
Benedetti, Valentin; Casini, Horacio German; Kawahigashi, Yasuyuki; Longo, Roberto; Magán, Javier M.; Modular invariance as completeness; Cornell University; ArXiv; 2024; 8-2024; 1-37
dc.identifier.issn
2331-8422
dc.identifier.uri
http://hdl.handle.net/11336/247877
dc.description.abstract
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.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Cornell University
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
MODULAR INVARIANCE
dc.subject
HAAG DUALITY
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COMPLETENESS
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CFT
dc.subject.classification
Física de Partículas y Campos
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Ciencias Físicas
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CIENCIAS NATURALES Y EXACTAS
dc.title
Modular invariance as completeness
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2024-11-01T11:27:22Z
dc.identifier.eissn
2331-8422
dc.journal.volume
2024
dc.journal.pagination
1-37
dc.journal.pais
Estados Unidos
dc.journal.ciudad
Ithaca
dc.description.fil
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
dc.description.fil
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
dc.description.fil
Fil: Kawahigashi, Yasuyuki. University of Tokyo; Japón
dc.description.fil
Fil: Longo, Roberto. Universita Tor Vergata; Italia
dc.description.fil
Fil: Magán, Javier M.. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
dc.journal.title
ArXiv
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2408.04011
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.48550/arXiv.2408.04011
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