Classification of operator algebraic conformal field theories

Details Classification of operator algebraic conformal field theories Classification of operator algebraic conformal field theories

2002-11-08

arxiv.org/abs/math/0211141v3

Mathematics

Operator Algebras

LaTeX 2e, 14 pages, more explanations added

Scientific paper

We give an exposition on the current status of classification of operator algebraic conformal field theories. We explain roles of complete rationality and alpha-induction for nets of subfactors in such a classification and present the current classification result, a joint work with R. Longo, for the case with central charge less than 1, where we have a complete classification list consisting of the Virasoro nets, their simple current extensions of index 2, and four exceptionals. Two of the four exceptionals appear to be new.

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