# Affine q -deformed symmetry and the classical Yang-Baxter σ -model

Delduc, F. (Université de Lyon, ENS de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342, Lyon, France) ; Kameyama, T. (Université de Lyon, ENS de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342, Lyon, France) ; Magro, M. (Université de Lyon, ENS de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342, Lyon, France) ; Vicedo, B. (School of Physics, Astronomy and Mathematics, University of Hertfordshire, College Lane, Hatfield, AL10 9AB, United Kingdom)

27 March 2017

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 q g ${U}_q\left(\mathfrak{g}\right)$ , with g $\mathfrak{g}$ 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 q L g ${U}_q\left(L\mathfrak{g}\right)$ , where L g $L\mathfrak{g}$ is the loop algebra of g $\mathfrak{g}$ . Quite unexpectedly, these defining relations are proved without encountering any ambiguity related to the non-ultralocality of this integrable σ -model.

Published in: JHEP 1703 (2017) 126