Local conformal nets arising from framed vertex operator algebras
type: Item
instance of: scholarly article
title: Local conformal nets arising from framed vertex operator algebras
zbMATH Open document ID: 1105.81052
author: Yasuyuki Kawahigashi
author: Roberto Longo
published in: Advances in Mathematics
publication date: 2006-11-15T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0407263
review text: Chiral conformal quantum field theory, where the unit circle serves as ``spacetime'', has been the subject of intense mathematical studies for many years. There are two approaches using infinite-dimensional algebraic systems. Either one starts from a local net of von Neumann algebras or from a vertex operator algebra. However, one rarely finds a comparison of the two approaches in the literature though both theories have mathematical objects in common such as the Virasoro algebra. The article fills the gap by explaining the relationship between the two. In particular, it provides a local net of von Neumann algebras corresponding to the ``moonshine'' vertex operator algebra of Frenkel-Lepowsky-Meurman. The net is shown to be trivial in the sense that the vacuum sector is the only irreducible Doplicher-Haag-Roberts sector. Its gauge group is known to be the Monster group, the largest among the (26) sporadic finite simple groups. Previously developed tools are employed such as \(\alpha\)-induction and complete rationality to study extensions of local nets.
reviewed by: Gert Roepstorff
Mathematics Subject Classification ID: 81T05
Mathematics Subject Classification ID: 81T40
Mathematics Subject Classification ID: 17B69
zbMATH DE Number: 5072578
zbMATH Keywords: algebraic quantum field theory
zbMATH Keywords: conformal field theory
zbMATH Keywords: Monster group
zbMATH Keywords: vertex operator algebra
MaRDI profile type: Publication
OpenAlex ID: W2058753575
arXiv ID: math/0407263
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DOI: 10.1016/J.AIM.2005.11.003
description: scientific article