Conformal blocks of Wess-Zumino-Witten model from its free-field representation
Abstract
A bstract A powerful approach to the celebrated Wess-Zumino-Witten (WZW) model is provided by its free-field realization. However, explicit calculations of conformal blocks are not described in the literature in full detail. We begin this study with the simplest cases of the $$ \hat{sl}{(2)}_k $$ sl ̂ 2 k and $$ \hat{sl}{(3)}_k $$ sl ̂ 3 k WZW models, with special emphasis on their global sl (2) and sl (3) symmetries of the resulting correlators, which are not explicit in this formalism. Also non-trivial is the verification of the Knizhnik-Zamolodchikov equations in the $$ \hat{sl}{(3)}_k $$ sl ̂ 3 k case, where the answers take the form of double integrals over screening charge positions and do not look like ordinary hypergeometric functions.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Quantum Mechanics and Non-Hermitian Physics
Nonlinear Waves and Solitons
Publication details
- Journal / source
- Journal of High Energy Physics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 2026
- Issue
- 8
- Publication date
- 13 August 2026
- Language
- EN