Correlators of primary fields in the SU(2) WZW theory on riemann surfaces

Abstract

We exhibit a method to obtain ordinary differential equations for correlation functions of primary fields in the SU(2) WZW theory, for arbitrary level k, on Rieman surfaces. The holomorphic, multivalued solutions of these equations are identified with the current blocks out of which the correlators are constructed. In some cases the germs of the current blocks satisfy certain polynomial equations which facilitate their determination. We discuss the monodromy and the moduli-dependent normalization the solution.