On the Hamiltonian integrability of the bi-Yang-Baxter sigma-model

Benoit Vicedo, Marc Magro, Francois Delduc, Sylvain Lacroix

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    Abstract

    The bi-Yang-Baxter σ-model is a certain two-parameter deformation of the principal chiral model on a real Lie group G for which the left and right G-symmetries of the latter are both replaced by Poisson-Lie symmetries. It was introduced by C. Klimčík who also recently showed it admits a Lax pair, thereby proving it is integrable at the Lagrangian level. By working in the Hamiltonian formalism and starting from an equivalent description of the model as a two-parameter deformation of the coset σ-model on G × G/Gdiag, we show that it also admits a Lax matrix whose Poisson bracket is of the standard r/s-form characterised by a twist function which we determine. A number of results immediately follow from this, including the identification of certain complex Poisson commuting Kac-Moody currents as well as an explicit description of the q-deformed symmetries of the model. Moreover, the model is also shown to fit naturally in the general scheme recently developed for constructing integrable deformations of σ-models. Finally, we show that although the Poisson bracket of the Lax matrix still takes the r/s-form after fixing the Gdiag gauge symmetry, it is no longer characterised by a twist function.
    Original languageEnglish
    JournalJournal of High Energy Physics (JHEP)
    Volume1603
    Issue number104
    DOIs
    Publication statusPublished - 15 Mar 2016

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