A construction of the \(c<1\) modular invariant partition functions
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)].
level one highest weight representations
two-dimensional conformal field theories
scientific article; zbMATH DE number 4079701
scientific article