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Fusion hierarchies, T-systems and Y-systems of logarithmic minimal models
Onglets principaux
2 takes the form of functional relations for D(u) and T(u) of polynomial degree p'. These derive from fusion hierarchies of commuting transfer tangles D^{m,n}(u) and T^{m,n}(u) where D(u)=D^{1,1}(u) and T(u)=T^{1,1}(u). The fused transfer tangles are constructed from (m,n)-fused face operators involving Wenzl-Jones projectors P_k on k=m or k=n nodes. Some projectors P_k are singular for k>p'-1, but we argue that D^{m,n}(u) and T^{m,n}(u) are well defined for all m,n. For generic lambda, we derive the fusion hierarchies and the associated T- and Y-systems. For the logarithmic theories, the closure of the fusion hierarchies at n=p' translates into functional relations of polynomial degree p' for D^{m,1}(u) and T^{m,1}(u). We also derive the closure of the Y-systems for the logarithmic theories. The T- and Y-systems are the key to exact integrability and we observe that the underlying structure of these functional equations relate to Dynkin diagrams of affine Lie algebras.
Type de document | Article de périodique (Journal article) – Article de recherche |
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Type d'accès | Accès interdit |
Année de publication | 2014 |
Langue | Anglais |
Information sur le périodique | "Journal of Statistical Mechanics: Theory and Experiment" - Vol. P10004, no.May 2014, p. 1-89 (2014) |
Peer reviewed | oui |
Editeur | Institute of Physics Publishing Ltd. ((United Kingdom) Bristol) |
e-issn | 1742-5468 |
Statut de la publication | Publié |
Affiliations | UCL - SST/IRMP - Institut de recherche en mathématique et physique |
Liens |
Référence bibliographique | Morin Duchesne, Alexi ; Pearce, Paul ; Rasmussen, Jørgen. Fusion hierarchies, T-systems and Y-systems of logarithmic minimal models. In: Journal of Statistical Mechanics: Theory and Experiment, Vol. P10004, no.May 2014, p. 1-89 (2014) |
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Permalien | http://hdl.handle.net/2078.1/170583 |