WARD IDENTITIES FOR AFFINE-VIRASORO CORRELATORS

Generalizing the Knizhnik-Zamolodchikov equations,we derive a hierarch y of nonlinear Ward identities for affine-Virasoro correlators. The hi erarchy follows from null states of the Knizhnik-Zamolodchikov type an d the assumption of factorization, whose consistency we verify at an a bstract level. Solution of the equations requires concrete factorizati on ansatze, which may vary over affine-Virasoro space. As a first exam ple, we solve the nonlinear equations for the coset constructions, usi ng a matrix factorization. The resulting coset correlators satisfy fir st-order linear partial differential equations whose solutions are the coset blocks defined by Douglas.