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

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Itsios, Georgios
Sfetsos, Konstantinos
Siampos, Konstantinos
Torrielli, Alessandro
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Abstract
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.
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Lax-pair, Yang–Baxter equation, Two-parameter deformation, Principal chiral model, WZW model, Non-Abelian T-dual, SCOAP3
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