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Yang-Baxter deformations of the principal chiral model plus Wess-Zumino term

Hoare, Ben and Lacroix, Sylvain (2020) 'Yang-Baxter deformations of the principal chiral model plus Wess-Zumino term.', Journal of physics A: mathematical and theoretical., 53 (50). p. 505401.


A large class of integrable deformations of the principal chiral model, known as the Yang–Baxter deformations, are governed by skew-symmetric R-matrices solving the (modified) classical Yang–Baxter equation. We carry out a systematic investigation of these deformations in the presence of the Wess–Zumino term for simple Lie groups, working in a framework that treats both inhomogeneous and homogeneous deformations on the same footing. After analysing the cohomological conditions under which such a deformation is admissible, we consider an action for the general Yang–Baxter deformation of the principal chiral model plus Wess–Zumino term and prove its classical integrability. We also show how the model is found from a number of alternative formulations: affine Gaudin models, $\mathcal{E}$-models, four-dimensional Chern–Simons theory and, for homogeneous deformations, non-abelian T-duality.

Item Type:Article
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Publisher statement:This is an author-created, un-copyedited version of an article published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at
Date accepted:23 October 2020
Date deposited:28 September 2021
Date of first online publication:23 November 2020
Date first made open access:23 November 2021

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