Quantum groups and WZNW models
The authors explain the appearance of \(R\)-matrices and quantum groups in chiral WZNW-models and discuss the meaning of invariance of rational conformal field theories under quantum group action. First they discuss the problem on a classical level, where instead of the quantum exchange algebra there is a Poisson loop Lie group \(LG\). The authors note that field theory is defined not only by the Lagrangian, but also by the boundary conditions on the input fields. They consider two types of boundary conditions in the classical case and show that these conditions are related to IRF and vertex models of the quantum theory and define two \(r\)-matrices in the classical case. The relation between these two matrices is discussed; action of the Poisson-Lie group \(G\) and interpretation of the invariance of the theory under this action. Then the authors consider the quantum exchange algebra in \(R\)-matrix form and its free field parametrization. It is described the action of the quantum groups and it is shown that the quantum group is derived as a right-hand symmetry of the WZNW model.
scientific article; zbMATH DE number 7596