The classical Yang–Baxter equation and the associated Yangian symmetry of gauged WZW-type theories

• Main Authors: Itsios, Georgios, Sfetsos, Konstantinos, Siampos, Konstantinos, Torrielli, Alessandro
• Other Authors: Ίτσιος, Γεώργιος
• Format: Journal (paper)
• Language: English
• Published: 2018
• Subjects: Lax-pair; Yang–Baxter equation; Two-parameter deformation; Principal chiral model; WZW model; Non-Abelian T-dual; SCOAP3; Απεικονίσεις Yang-Baxter

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.