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

TL;DR

This paper explores how three-point functions in Wess-Zumino-Witten models depend on the level, revealing a connection with Berenstein-Zelevinsky triangles and fusion multiplicities, and explaining their construction and level-dependence.

Contribution

It introduces a method to construct three-point functions based on level-dependence and their relation to fusion multiplicities using Berenstein-Zelevinsky triangles.

Findings

Level-dependence of three-point functions mirrors fusion multiplicities.

Berenstein-Zelevinsky triangles correspond to three-point functions.

Threshold level plays a key role in the structure of 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.