We apply an idea of framed vertex operator algebras to a construction of local conformal nets of (injective type III1_) 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.
Kawahigashi, Y., Longo, R. (2006). Local conformal nets arising from framed vertex operator algebras. ADVANCES IN MATHEMATICS, 206(2), 729-751 [10.1016/j.aim.2005.11.003].
Local conformal nets arising from framed vertex operator algebras
LONGO, ROBERTO
2006-01-01
Abstract
We apply an idea of framed vertex operator algebras to a construction of local conformal nets of (injective type III1_) 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.