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

Benoit Vicedo; Marc Magro; Francois Delduc; Takashi Kameyama

doi:10.1007/JHEP03(2017)126

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

Benoit Vicedo, Marc Magro, Francois Delduc, Takashi Kameyama

Mathematics

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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 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 language	English
Number of pages	18
Journal	Journal of High Energy Physics
Volume	2017
Issue number	126
DOIs	https://doi.org/10.1007/JHEP03(2017)126
Publication status	Published - 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.

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Cite this

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title = "Affine q-deformed symmetry and the classical Yang-Baxter σ-model",

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 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.",

author = "Benoit Vicedo and Marc Magro and Francois Delduc and Takashi Kameyama",

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AU - Vicedo, Benoit

AU - Magro, Marc

AU - Delduc, Francois

AU - Kameyama, Takashi

N1 - 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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N2 - 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.

AB - 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.

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