Quantum su(n)_k monodromy matrices

TL;DR

This paper investigates the quantum properties of monodromy matrices in the SU(n) WZNW model, focusing on renormalization factors and their compatibility with quantum determinants, advancing understanding of quantum group structures.

Contribution

It analyzes the renormalization of quantum monodromy matrices in SU(n) WZNW models and demonstrates their compatibility with quantum determinants, linking algebraic and field-theoretic perspectives.

Findings

Renormalization factors are necessary for consistent quantization.

Quantum determinants maintain factorization property despite non-commutativity.

Compatibility between renormalization and quantum determinant definitions is established.

Abstract

The canonical quantization of the chiral Wess-Zumino-Novikov-Witten (WZNW) monodromy matrices (both the diagonal and the general one) requires additional numerical factors that can be attributed to renormalization. We discuss, for G=SU(n), the field-theoretic and algebraic aspects of this phenomenon and show that these renormalization factors are compatible with the natural definitions of quantum determinants possessing the factorization property (i.e., the determinant of a product is equal to the product of determinants, which is a non-trivial fact for matrices with non-commuting entries).