Abstract (Elsevier)
A number of issues concerning affine Lie algebras and string propagation on group manifolds are addressed. We show that a 1 + 1 dimensional quantum field theory which gives a realization of current algebra (for any non-abelian Lie group G) will always give rise to an “integrable” representation. It is known that string propagation on the group manifold can give rise to a realization of current algebra for any G and any k , but precisely which representations occur for given k has not been determined previously. We do this here by studying modular invariance and by making a semiclassical study for large k . These results permit a complete description of the operator product algebra. Some examples based on SO(3) and SU(3)/Z 3 are worked out in detail.