ABSTRACT
The chapter introduces the Wess-Zumino-Witten (WZW) model, including its current algebra. It reviews affine Kac-Moody algebras, where some background on simple Lie algebras is also provided. The chapter discusses applications, especially 3-point functions and fusion rules. It shows how a priori surprising mathematical properties of the algebras find a natural framework in WZW models, and their duality as rational conformal field theories. A more direct significance, in terms of the roots of the algebra, can be given to the Cartan matrix and Coxeter-Dynkin diagrams. The economy allowed the discovery of the Kac-Moody algebras: it was natural to wonder whether loosening the constraints on the Cartan matrix would lead to other interesting types of algebras. The price to be paid is the imposition of the more complicated Serre relations. But these relations are what ensure that a finite-dimensional algebra is generated.
