Classification of subsystems for the Haag-Kastler nets generated by \(c=1\) chiral current algebras
type: Item
instance of: scholarly article
title: Classification of subsystems for the Haag-Kastler nets generated by \(c=1\) chiral current algebras
zbMATH Open document ID: 0946.47055
DOI: 10.1023/A:1007517131143
author: Sebastiano Carpi
published in: Letters in Mathematical Physics
publication date: 2000-10-17T00:00:00Z
review text: In the algebraic approach to quantum field theory, the objects under investigation are local nets of von Neumann algebras (Haag-Kastler nets). This paper studies the classification of the \(SL(2, { R})\)-covariant subsystems of Haag-Kastler nets constructed from two models of chiral conformal field theory, the \(\widehat{u}(1)\) and the \(\widehat{su}(2)_1\) chiral current algebras. The author finds that there is a one-to-one correspondence between subsystems of the Haag-Kastler net \({\mathcal F}\) corresponding to the \(\widehat{su}(2)_1\) chiral current algebra and nets \({\mathcal F}^H\) consisting of the local algebras generated by local operators invariant under some closed subgroup \(H\) of the gauge automorphisms group \(SO(3)\) of \({\mathcal F}\). In the case of the Haag-Kastler net \({\mathcal F}_1\) generated by the \(\widehat{u}(1)\) chiral current it is shown that there are exactly two distinct proper subsystems, one generated by the energy-momentum tensor and the gauge invariant subsystem \({\mathcal F}_1^{Z_2}\). The paper concludes with a discussion of the possible generalizations of the approach presented in the paper to other models.
reviewed by: Oliver Rudolph
Mathematics Subject Classification ID: 47N50
Mathematics Subject Classification ID: 81T05
Mathematics Subject Classification ID: 81T40
zbMATH DE Number: 1334611
zbMATH Keywords: Haag-Kastler Net
zbMATH Keywords: chiral current algebra
zbMATH Keywords: chiral conformal field theory
zbMATH Keywords: classification of the \(SL(2,R)\)-covariant subsystems
MaRDI profile type: Publication
full work available at URL: a:1007517131143
OpenAlex ID: W17745358
description: scientific article; zbMATH DE number 1334611