University of Hertfordshire

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

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  • Benoit Vicedo
  • Francois Delduc
  • Marc Magro
  • Takashi Kameyama
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Original languageEnglish
Number of pages18
JournalJournal of High Energy Physics
Publication statusPublished - 23 Mar 2017


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 Uq(g)Uq(g) , with gg 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 Uq(Lg)Uq(Lg) , where LgLg is the loop algebra of gg . Quite unexpectedly, these defining relations are proved without encountering any ambiguity related to the non-ultralocality of this integrable σ-model.


Open Access: This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. © 2017 The Authors. Article funded by SCOAP. .

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