Classification of Local Conformal Nets. Case c < 1
Abstract
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 AD_{2n}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 CappelliItzyksonZuber and the method of alphainduction 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.
 Publication:

arXiv eprints
 Pub Date:
 January 2002
 arXiv:
 arXiv:mathph/0201015
 Bibcode:
 2002math.ph...1015K
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 Mathematics  Operator Algebras;
 81T40;
 46L37;
 17B68 (Primary);
 81T08;
 46L60;
 22E67;
 81R10 (Secondary)
 EPrint:
 30 pages, LaTeX2e