Affine q-deformed symmetry and the classical Yang-Baxter \u03c3-model

Abstract

The Yang-Baxter σ-model is an integrable deformation of the principal chiral model on a Lie group G. The deformation breaks the G × G symmetry to U(1)rank(G) × G. It is known that there exist non-local conserved charges which, together with the unbroken U(1)rank(G) local charges, form a Poisson algebra , which is the semiclassical limit of the quantum group {U}_qleft(mathfrak{g}right) , with mathfrak{g} the Lie algebra of G. For a general Lie group G with rank(G) > 1, we extend the previous result by constructing local and non-local conserved charges satisfying all the defining relations of the infinite-dimensional Poisson algebra , the classical analogue of the quantum loop algebra {U}_qleft(Lmathfrak{g}right) , where Lmathfrak{g} is the loop algebra of mathfrak{g} . Quite unexpectedly, these defining relations are proved without encountering any ambiguity related to the non-ultralocality of this integrable σ-model.