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

Hoare, Ben; Lacroix, Sylvain

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Authors

Sylvain Lacroix



Abstract

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.

Citation

Hoare, B., & Lacroix, S. (2020). Yang-Baxter deformations of the principal chiral model plus Wess-Zumino term. Journal of Physics A: Mathematical and Theoretical, 53(50), Article 505401. https://doi.org/10.1088/1751-8121/abc43d

Journal Article Type Article
Acceptance Date Oct 23, 2020
Online Publication Date Nov 23, 2020
Publication Date Dec 18, 2020
Deposit Date Sep 13, 2021
Publicly Available Date Mar 29, 2024
Journal Journal of Physics A: Mathematical and Theoretical
Print ISSN 1751-8113
Electronic ISSN 1751-8121
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 53
Issue 50
Article Number 505401
DOI https://doi.org/10.1088/1751-8121/abc43d
Related Public URLs https://arxiv.org/abs/2009.00341

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Copyright 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 https://doi.org/10.1088/1751-8121/abc43d





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