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2015

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

Delduc, Francois, Lacroix, Sylvain, Magro, Marc et al.

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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 / G_diag, 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.

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

Built on

J. M. Maillet, Kac-Moody algebra and extended Yang-Baxter relations in the O ⁡ ( N ) O(N) non-linear sigma model
1985
Earlier work this paper cites.
J. M. Maillet, New integrable canonical structures in two-dimensional models
1986
Earlier work this paper cites.
B.-Y. Hou, B.-Y. Hou, Y.-W. Li, and B. Wu, The Poisson-Lie structure of nonlinear O(N) sigma model by using the moving frame method
1994
Earlier work this paper cites.
A. Sevostyanov, The Classical R R matrix method for nonlinear sigma model
1996
Earlier work this paper cites.
C. Klimcik, Yang-Baxter sigma models and dS/AdS T duality
2002
Earlier work this paper cites.
C. Klimcik, On integrability of the Yang-Baxter σ \sigma -model
Original
2009
Earlier work this paper cites.
M. Magro, The classical exchange algebra of A d S 5 × S 5 AdS_{5}\times S^{5} string theory
Original
2009
Earlier work this paper cites.
B. Vicedo, Hamiltonian dynamics and the hidden symmetries of the A d S 5 × S 5 AdS_{5}\times S^{5} superstring
Original
2010
Earlier work this paper cites.
B. Vicedo, The classical R-matrix of AdS/CFT and its Lie dialgebra structure
Original
2011
Earlier work this paper cites.
I. Kawaguchi and K. Yoshida, Hybrid classical integrability in squashed sigma models
Original
2011
Earlier work this paper cites.
I. Kawaguchi, T. Matsumoto, and K. Yoshida, On the classical equivalence of monodromy matrices in squashed sigma model
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2012
Earlier work this paper cites.
F. Delduc, M. Magro, and B. Vicedo, Alleviating the non-ultralocality of coset sigma models through a generalized Faddeev-Reshetikhin procedure
Original
2012
Earlier work this paper cites.
S. L. Lukyanov, The integrable harmonic map problem versus Ricci flow
Original
2012
Earlier work this paper cites.
F. Delduc, M. Magro, and B. Vicedo, On classical q q -deformations of integrable σ \sigma -models
Original
2013
Earlier work this paper cites.

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