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

• Published in: The journal of high energy physics 2017-03, Vol.2017 (3), p.1-19, Article 126
• Main Authors: Delduc, F., Kameyama, T., Magro, M., Vicedo, B.
• Format: Article
• Language: English
• Subjects: Algebra; Ambiguity; Analogue; Classical and Quantum Gravitation; Deformation; Elementary Particles; High Energy Physics - Theory; Lie groups; Mathematical models; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Symmetry; Texts
• ISSN: 1029-8479; 1126-6708; 1029-8479
• DOI: 10.1007/JHEP03(2017)126

A bstract 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 , with 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 , where L g is the loop algebra of g . Quite unexpectedly, these defining relations are proved without encountering any ambiguity related to the non-ultralocality of this integrable σ -model.