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. 1 Introduction Yangian symmetries are expected to play a major role in our understanding of the integrable structure of conformal field theories and their deformations [1, 2]. Some conformal field theories are known to exhibit a Yangian symmetry for any affine Lie algebra at the critical point, with a level-independent structure [3, 4, 5]. The Yangian generators of that symmetry are understood as quantum extensions of classical non-local charges, such as those found in the non-linear sigma model and current algebra models [6]-[15]. Therefore the study of classical algebras of non-local charges may be regarded as a pre-quantum step toward the comprehension of symmetry and integrability properties of this class of field theories. In previous works [16, 17], we have studied the algebra of the infinite non-local conserved charges in the O(N) non-linear sigma model. The Wess-Zumino-Novikov-Witten (WZNW) model is also known to display an infinite set of non-local charges [18], and the primary aim of this paper is to unveil the classical algebra generated by them. In particular, we are interested in the dependence of this algebra with respect to the Wess-Zumino coupling