Classification of Local Conformal Nets. Case c < 1
by
Yasuyuki Kawahigashi
University of Tokyo
Coauthors: Roberto Longo

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.

Paper reference: arXiv:math-ph/0201015

Date received: June 2, 2002