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dc.contributor.author
Benedetti, Valentin  
dc.contributor.author
Casini, Horacio German  
dc.contributor.author
Kawahigashi, Yasuyuki  
dc.contributor.author
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  
dc.subject.classification
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