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

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.

1+32 pages, Latex, v2: few minor changes, NPB version, v3: A factor of two corrected in (A.22)

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• The all-loop non-Abelian Thirring model and its RG flow
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• On the Integrable Structure of the SU(2) Wess-Zumino-Novikov-Witten Model
• Yang-Baxter deformations and string dualities