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

Benoit Vicedo, Marc Magro, Francois Delduc, Takashi Kameyama

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Number of pages18
JournalJournal of High Energy Physics
Issue number126
Publication statusPublished - 23 Mar 2017

Bibliographical note

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.

Cite this