Some Correlators of SU(3)₃ WZW Models on Higher-Genus Riemann Surfaces

Using the conformal embedding on the torus, we can express some characters of $SU(3)_3$ in terms of $SO(8)_1$ characters. Then with the help of crossing symmetry, modular transformation and factorization properties of Green functions, we will calculate a class of correlators of $SU(3)_3$ on arbitrary Riemann surfaces. This method can apply to all $k>1$ WZW models which can be conformally embedded in some $k=1$ WZW models.