Fusion coefficients in minimal conformal field theory

Abstract

In vector-like conformal field theory ($A_{p``-1},\;\;A_{p-1}$), all fusion coefficients are determined by solving second-order differential equations with monodromy condition and crossing symmetry. In this paper we extend this idea to chiral theory, and some fusion coefficients are expressed as the direct product of those of vector-like theory with undertimined sign ambiguity. But others some of fusion coefficients cannot be obtained by solving second order differential equations. These are explicitly demonstrated in three-state Potts Model (D$_4$, A$_4$).