Local conformal nets arising from framed vertex operator algebras
摘要
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.
引用
@article{arxiv.math/0407263,
title = {Local conformal nets arising from framed vertex operator algebras},
author = {Yasuyuki Kawahigashi and Roberto Longo},
journal= {arXiv preprint arXiv:math/0407263},
year = {2007}
}
备注
24 pages; The automorphism group of the moonshine net is now identified with the monster group