A new tool in the classification of rotational conformal field theories

The fact that in any rational conformal field theory (RCFT) four-point functions on the sphere must satisfy an ordinary differential equation gives a simple condition on the conformal dimensions of primary fields. We discuss how this can help in the classification program of RCFT. As an example all associative fusion rules with less than four non-trivial primary fields and Nijk ≤ 1 are discussed. Another application to the classification of chiral algebras is briefly mentioned. (orig.)