Abstract
We develop a general method for deriving ordinary differential equations for the correlators of primary and secondary fields in any rational conformal field theory on the torus, using the fusion rules and the conformal dimensions of the primary fields. Specific examples are worked out for minimal conformal field theories and Wess-Zumino-Witten models. We also show how to derive differential equations for the characters of a rational conformal field theory. The method is equally applicable for deriving differential equations for the correlation functions of the plane, and may be useful for the classification of all rational field theories.
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