Differential equation for genus-two characters in arbitrary rational conformal field theories

We develop a general method for deriving ordinary differential equations for the genus-two "characters" of an arbitrary rational conformal field theory using the hyperelliptic representation of the genus-two moduli space. We illustrate our method by explicitly deriving the character differential equations for k=1 SU (2), G<SUB>2</SUB> and F<SUB>4</SUB>WZW models. Our method provides an intrinsic definition of conformal field theories on higher genus Riemann surfaces