Local conformal nets arising from framed vertex operator algebras

Details Local conformal nets arising from framed vertex operator algebras Local conformal nets arising from framed vertex operator algebras

2004-07-15

arxiv.org/abs/math/0407263v2

Adv. Math. 206 (2006), 729-751.

Mathematics

Operator Algebras

24 pages; The automorphism group of the moonshine net is now identified with the monster group

Scientific paper

10.1016/j.aim.2005.11.003

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.

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