On the Liouville coupling constants

Abstract

For the general operator product algebra coefficients derived by Cremmer Roussel Schnittger and the present author with (non-negative) integer screening numbers, the coupling constants determine the factors additional to the quantum group 6 j symbols. They are given by path independent products over a two-dimensional lattice in the zero mode space. It is shown that the ansatz for the three-point function of Dorn-Otto and Zamolodchikov-Zamolodchikov precisely defines the corresponding flat lattice connection, so that it does give a natural generalization of these coupling constants to continuous screening numbers. The consistency of the restriction to integer screening charges is reviewed, and shown to be linked with the orthogonality of the (generalized) 6 j symbols. Thus extending this last relation is the key to general screening numbers.