• DOI:10.1007/JHEP03(2017)126
• Corpus ID: 119102258

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

@article{Delduc2017AffineQS,
  title={Affine q-deformed symmetry and the classical Yang-Baxter $\sigma$-model},
  author={F. Delduc and T. Kameyama and M. Magro and B. Vicedo},
  journal={Journal of High Energy Physics},
  year={2017},
  volume={2017},
  pages={1-19}
}

• F. Delduc, T. Kameyama, +1 author B. Vicedo
• Published 13 January 2017
• Mathematics
• Journal of High Energy Physics

A bstractThe 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 Uqg$$ {U}_q\left(\mathfrak{g}\right) $$, 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 UqLg$$ {U}_q\left(L\mathfrak{g}\right) $$, where Lg$$ L\mathfrak{g} $$ 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.