We completely classify diffeomorphism covariant local nets of von Neumann algebras on the circle with central charge c less than 1. The irreducible ones are in bijective correspondence with the pairs of A-D2n-E 6,8 Dynkin diagrams such that the difference of their Coxeter numbers is equal to 1. We first identify the nets generated by irreducible representations of the Virasoro algebra for c < 1 with certain coset nets. Then, by using the classification of modular invariants for the minimal models by Cappelli-Itzykson-Zuber and the method of α-induction in subfactor theory, we classify all local irreducible extensions of the Virasoro nets for c < 1 and infer our main classification result. As an application, we identify in our classification list certain concrete coset nets studied in the literature.
Kawahigashi, Y., & Longo, R. (2004). Classification of local conformal nets. Case c < 1. ANNALS OF MATHEMATICS, 160(2), 493-522.
Tipologia: | Articolo su rivista |
Citazione: | Kawahigashi, Y., & Longo, R. (2004). Classification of local conformal nets. Case c < 1. ANNALS OF MATHEMATICS, 160(2), 493-522. |
Lingua: | English |
Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica |
Revisione (peer review): | Sì, ma tipo non specificato |
Tipo: | Articolo |
Rilevanza: | Rilevanza internazionale |
Stato di pubblicazione: | Pubblicato |
Data di pubblicazione: | 2004 |
Titolo: | Classification of local conformal nets. Case c < 1 |
Autori: | |
Autori: | Kawahigashi, Y; Longo, R |
Appare nelle tipologie: | 01 - Articolo su rivista |