Fractional-level current algebras and the classification of characters

Abstract

We point out some interesting relationships between the characters of non-unitary and unitary rational conformal field theories. For Â₁ Kac-Moody algebras of fractional level m, the residues of the characters at the pole in z correspond to the Virasoro characters for the c<1 minimal models. The relationship between the Kac-Moody and Virasoro central charges is precisely that found by Knizhnik, Polyakov and Zamolodchikov in the context of two-dimensional gravity. The finite parts of the non-unitary Â₁ characters are also closely related to other RCFT, and it is shown how they fit in to a scheme for classifying RCFT and representing their characters by Feigin-Fuchs contour integrals.