Local conformal nets arising from framed vertex operator algebras |
| |
Authors: | Yasuyuki Kawahigashi Roberto Longo |
| |
Institution: | a Department of Mathematical Sciences, University of Tokyo, Komaba, Tokyo 153-8914, Japan b Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, I-00133 Roma, Italy |
| |
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 α-induction and complete rationality to study extensions of local conformal nets. |
| |
Keywords: | Algebraic quantum field theory Conformal field theory Monster Moonshine Vertex operator algebra Subfactor |
本文献已被 ScienceDirect 等数据库收录! |
|