Chiral Quantization of the WZW $SU(n)$ Model

TL;DR

This paper presents a chiral quantization approach for the $SU(n)$ WZW model, comparing it with algebraic methods and verifying the vertex operator algebra through KZ equations.

Contribution

It introduces a chiral quantization framework for the $SU(n)$ WZW model and validates it against existing algebraic results.

Findings

Successful quantization using chiral variables

Verification of vertex operator algebra via KZ equations

Comparison with algebraic approaches confirms consistency

Abstract

We quantize the $SU(n)$ Wess-Zumino-Witten model in terms of left and right chiral variables choosing an appropriate gauge and we compare our results with the results that have been previously obtained in the algebraic treatment of the problem. The algebra of the chiral vertex operators in the fundamental representation is verified by solving appropriate Knizhnik-Zamolodchikov equations.