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

  • F. DelducEmail author
  • T. Kameyama
  • M. Magro
  • B. Vicedo
Open Access
Regular Article - Theoretical Physics

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 Open image in new window , which is the semiclassical limit of the quantum group \( {U}_q\left(\mathfrak{g}\right) \), with \( \mathfrak{g} \) 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 Open image in new window , the classical analogue of the quantum loop algebra \( {U}_q\left(L\mathfrak{g}\right) \), where \( L\mathfrak{g} \) is the loop algebra of \( \mathfrak{g} \). Quite unexpectedly, these defining relations are proved without encountering any ambiguity related to the non-ultralocality of this integrable σ-model.

Keywords

Integrable Field Theories Sigma Models 

Notes

Open Access

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Université de Lyon, ENS de Lyon, Université Claude Bernard, CNRS, Laboratoire de PhysiqueLyonFrance
  2. 2.School of Physics, Astronomy and MathematicsUniversity of HertfordshireHatfieldUnited Kingdom

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