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 A-D_{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 Cappelli-Itzykson-Zuber and the method of alpha-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.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2002
- DOI:
- 10.48550/arXiv.math-ph/0201015
- arXiv:
- arXiv:math-ph/0201015
- Bibcode:
- 2002math.ph...1015K
- Keywords:
-
- Mathematical Physics;
- High Energy Physics - Theory;
- Mathematics - Operator Algebras;
- 81T40;
- 46L37;
- 17B68 (Primary);
- 81T08;
- 46L60;
- 22E67;
- 81R10 (Secondary)
- E-Print:
- 30 pages, LaTeX2e