The classical Yang–Baxter equation and the associated Yangian symmetry of gauged WZW-type theories
Georgios Itsios (Department of Mathematics, University of Patras, Patras, 26110, Greece); Konstantinos Sfetsos (Department of Nuclear and Particle Physics, Faculty of Physics, University of Athens, Athens, 15771, Greece); Konstantinos Siampos (Mécanique et Gravitation, Université de Mons, Mons, 7000, Belgium); Alessandro Torrielli (Department of Mathematics, University of Surrey, Guildford, GU2 7XH, UK)
We construct the Lax-pair, the classical monodromy matrix and the corresponding solution of the Yang–Baxter equation, for a two-parameter deformation of the Principal chiral model for a simple group. This deformation includes as a one-parameter subset, a class of integrable gauged WZW-type theories interpolating between the WZW model and the non-Abelian T-dual of the principal chiral model. We derive in full detail the Yangian algebra using two independent methods: by computing the algebra of the non-local charges and alternatively through an expansion of the Maillet brackets for the monodromy matrix. As a byproduct, we also provide a detailed general proof of the Serre relations for the Yangian symmetry.
