SOLVING THE WARD IDENTITIES OF IRRATIONAL CONFORMAL FIELD-THEORY

The affine-Virasoro Ward identities are a system of nonlinear differential equations which describe the correlators of all affine-Virasoro constructions, including rational and irrational conformal field theory. We study the Ward identities in some detail, with several central results. First, we solve for the correlators of the affine-Sugawara nests, which are associated with the nested subgroups g superset of h(1) superset of ... superset of h(n). We also find an equivalent algebraic formulation which allows us to obtain global solutions across the set of all affine-Virasoro constructions. A particular global solution is discussed which gives the correct nest correlators, exhibits braiding for all affine-Virasoro correlators, and shows good physical behavior, at least for four-point correlators at high level on simple g. In rational and irrational conformal field theory, the high-level fusion rules of the broken affine modules follow the Clebsch-Gordan coefficients of the representations.