Classification of Local Conformal Nets. Case c < 1

Details Classification of Local Conformal Nets. Case c < 1 Classification of Local Conformal Nets. Case c < 1

2002-01-08

arxiv.org/abs/math-ph/0201015v3

Annals of Mathematics 160 (2004), 493-522

Physics

Mathematical Physics

30 pages, LaTeX2e

Scientific paper

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.

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