Verlinde Algebras and the Intersection Form on Vanishing Cycles

TL;DR

This paper proves Zuber's conjecture linking the fusion rules of the $su(N)_k$ WZW model in conformal field theory with the intersection form on vanishing cycles of a related fusion potential.

Contribution

It establishes a rigorous connection between fusion rules in conformal field theory and algebraic geometry through the intersection form on vanishing cycles.

Findings

Proof of Zuber's conjecture.

Connection between fusion rules and intersection forms.

Advancement in understanding the algebraic structure of WZW models.

Abstract

We prove Zuber's conjecture establishing connections of the fusion rules of the $su(N)_k$ WZW model of conformal field theory and the intersection form on vanishing cycles of the associated fusion potential.