On the level-dependence of Wess-Zumino-Witten three-point functions

Abstract

Three-point functions of Wess-Zumino-Witten models are investigated. In particular, we study the level-dependence of three-point functions in the models based on algebras $su(3)$ and $su(4)$. We find a correspondence with Berenstein-Zelevinsky triangles. Using previous work connecting those triangles to the fusion multiplicities, and the Gepner-Witten depth rule, we explain how to construct the full three-point functions. We show how their level-dependence is similar to that of the related fusion multiplicity. For example, the concept of threshold level plays a prominent role, as it does for fusion.