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Local conformal nets arising from framed vertex operator algebras | | Yasuyuki Kawahigashi
; Roberto Longo
; | | Date: |
15 Jul 2004 | | Subject: | Operator Algebras; Mathematical Physics; Quantum Algebra MSC-class: 81R15; 81T05; 81T40; 46L37; 17B69; 20D08 | math.OA math-ph math.MP math.QA | | Abstract: | We apply an idea of framed vertex operator algebras to a construction of local conformal nets of (injective type III_1) factors on the circle corresponding to various lattice vertex operator algebras and their twisted orbifolds. In particular, we give a local conformal net corresponding to the moonshine vertex operator algebras of Frenkel-Lepowsky-Meurman. Its central charge is 24, it has a trivial representation theory in the sense that the vacuum sector is the only irreducible DHR sector, its vacuum character is the modular invariant J-function and its automorphism group (the gauge group) is the Monster group. We use our previous tools such as alpha-induction and complete rationality to study extensions of local conformal nets. | | Source: | arXiv, math.OA/0407263 | | Services: | Forum | Review | PDF | Favorites | |
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