Soliton strings, the WZW model and modular invariance

It is shown that a theory of strings on a nonsimply-connected group manifold has a soliton sector that is essential for modular invariance. A semiclassical analysis of this sector is used to reduce the problem of determining the representations of the Kac-Moody algebra that appear in the theory to the relatively easy task of finding the representations of the related finite algebra that satisfy certain simple conditions. Some examples are worked out in detail, including the case of SO(3), where it is shown that half-integer representations occur for odd k/2, and the case of SU(3)/Z3 for the first few values of k. The k = 1 SO(N) and SU(N) theories are also considered. (orig.)