The anisotropic \lambda-deformed SU(2) model is integrable

TL;DR

This paper proves the classical integrability of the anisotropic mbda-deformed SU(2) model by constructing its Lax pair, symmetry algebra, and r/s matrices, linking it to known models and equations.

Contribution

It demonstrates the classical integrability of the anisotropic mbda-deformed SU(2) model and derives its algebraic structures, including the Lax pair and r/s matrices.

Findings

Established the Lax pair formulation for the model.

Derived the symmetry current algebra and Poisson brackets.

Provided solutions to the modified Yang-Baxter equation.

Abstract

The all-loop anisotropic Thirring model interpolates between the WZW model and the non-Abelian T-dual of the anisotropic principal chiral model. We focus on the SU(2) case and we prove that it is classically integrable by providing its Lax pair formulation. We derive its underlying symmetry current algebra and use it to show that the Poisson brackets of the spatial part of the Lax pair, assume the Maillet form. In this way we procure the corresponding r and s matrices which provide non-trivial solutions to the modified Yang-Baxter equation.