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Classification of Two-dimensional Local Conformal Nets with c<1 and 2-cohomology Vanishing for Tensor Categories | Yasuyuki Kawahigashi
; Roberto Longo
; | Date: |
14 Apr 2003 | Journal: | Commun.Math.Phys. 244 (2004) 63-97 | Subject: | Mathematical Physics; Operator Algebras; Quantum Algebra MSC-class: 81T05, 81T40, 46L60, 18D10 | math-ph hep-th math.MP math.OA math.QA | Abstract: | We classify two-dimensional local conformal nets with parity symmetry and central charge less than 1, up to isomorphism. The maximal ones are in a bijective correspondence with the pairs of A-D-E Dynkin diagrams with the difference of their Coxeter numbers equal to 1. In our previous classification of one-dimensional local conformal nets, Dynkin diagrams D_{2n+1} and E_7 do not appear, but now they do appear in this classification of two-dimensional local conformal nets. Such nets are also characterized as two-dimensional local conformal nets with mu-index equal to 1 and central charge less than 1. Our main tool, in addition to our previous classification results for one-dimensional nets, is 2-cohomology vanishing for certain tensor categories related to the Virasoro tensor categories with central charge less than 1. | Source: | arXiv, math-ph/0304022 | Services: | Forum | Review | PDF | Favorites |
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