Artículo
Modular invariance as completeness
Benedetti, Valentin
; Casini, Horacio German
; Kawahigashi, Yasuyuki; Longo, Roberto; Magán, Javier M.
Fecha de publicación:
08/2024
Editorial:
Cornell University
Revista:
ArXiv
ISSN:
2331-8422
e-ISSN:
2331-8422
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
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.
Palabras clave:
MODULAR INVARIANCE
,
HAAG DUALITY
,
COMPLETENESS
,
CFT
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Articulos(CCT - PATAGONIA NORTE)
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - PATAGONIA NORTE
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - PATAGONIA NORTE
Citación
Benedetti, Valentin; Casini, Horacio German; Kawahigashi, Yasuyuki; Longo, Roberto; Magán, Javier M.; Modular invariance as completeness; Cornell University; ArXiv; 2024; 8-2024; 1-37
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