2015/12/31 by Francois Delduc, Sylvain Lacroix, Marc Magro +1 · 1 citation
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1007/jhep03(2016)104
published as JHEP 1603 (2016) 104 · 26 pages, 1 figure
arxiv created 2016/02/05 · arxiv updated 2017/07/06
The bi-Yang-Baxter sigma-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. Klimcik 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 sigma-model on G x 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 sigma-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.