A construction of the \(c<1\) modular invariant partition functions
type: Item
instance of: scholarly article
title: A construction of the \(c<1\) modular invariant partition functions
zbMATH Open document ID: 0661.17019
DOI: 10.1007/BF01218579
author: Daniel Altschüler
author: Korkut Bardakci
author: E. Rabinovici
published in: Communications in Mathematical Physics
publication date: 1988-01-01T00:00:00Z
review text: In a previous paper [\textit{K. Bardakci}, \textit{E. Rabinovici} and \textit{B. Säring}, Nucl. Phys. B 299, No.1, 151-182 (1988; Zbl 0661.17018)], two- dimensional conformal field theories, i.e. unitary representations of the direct sum of two copies of the Virasoro algebra, were constructed by tensoring discrete series representations. It was shown that all the models of types A and D can be obtained in this way [for the classification of such models, see \textit{A. Cappelli}, \textit{C. Itzykson} and \textit{J.-B. Zuber}, Modular invariant partition functions in two dimensions, Nucl. Phys. B 280, 445-465 (1987; Zbl 0661.17017)]. The present paper shows that the exceptional E types can also be obtained. It also proves a result which describes the decomposition of the restriction of the four spin representations of the affine algebra of \({\mathfrak o}(4n)\) to a certain subalgebra, which is used in the coset construction of the discrete series representations [\textit{P. Goddard}, \textit{A. Kent} and \textit{D. Olive}, Phys. Lett. B 152, 88-92 (1985; Zbl 0661.17015)].
reviewed by: Andrew N. Pressley
Mathematics Subject Classification ID: 17B65
Mathematics Subject Classification ID: 81T40
Mathematics Subject Classification ID: 17B67
zbMATH DE Number: 4079701
zbMATH Keywords: exceptional types
zbMATH Keywords: central charge
zbMATH Keywords: level one highest weight representations
zbMATH Keywords: affine O(4N) algebra
zbMATH Keywords: two-dimensional conformal field theories
zbMATH Keywords: Virasoro algebra
zbMATH Keywords: Modular invariant partition functions
zbMATH Keywords: decomposition
zbMATH Keywords: four spin representations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4079701