Algebra of non-local charges in the O(N) WZNW model at and beyond criticality

We derive the classical algebra of the non-local conserved charges in the O(N) WZNW model and analyze its dependence on the coupling constant of the Wess-Zumino term. As in the non-linear sigma model, we find cubic deformations of the O(N) affine algebra. The surprising result is that the cubic algebra of the WZNW non-local charges does not obey the Jacobi identity, thus opposing our expectations from the known Yangian symmetry of this model.