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.

24 pages, no figures

References in corpus (4)

• Generating-function method for fusion rules
• Fusion multiplicities as polytope volumes: N-point and higher-genus su(2) fusion
• Generating-function method for tensor products
• su(N) tensor product multiplicities and virtual Berenstein-Zelevinsky triangles

Cited by in corpus (5)

• Fusion multiplicities as polytope volumes: N-point and higher-genus su(2) fusion
• Affine su(3) and su(4) fusion multiplicities as polytope volumes
• Higher-genus su(N) fusion multiplicities as polytope volumes
• N-point and higher-genus osp(1|2) fusion
• Purely affine elementary su(N) fusions