2002/11/08 by Yasuyuki Kawahigashi, Kawahigashi, Yasuyuki
Mathematics · Physics and Astronomy · #46L37 #81T05 #81T40 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #math-ph #math.MP #math.OA #msc:46L37 #msc:81T05 #msc:81T40
paper · pdf · doi:10.48550/arxiv.math/0211141
LaTeX 2e, 14 pages, more explanations added
arxiv created 2003/04/16 · arxiv updated 2009/11/30
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.