Yang-Baxter deformations of the Principal Chiral Model plus Wess-Zumino term

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, E-models, 4-dimensional Chern-Simons theory and, for homogeneous deformations, non-abelian T-duality.

45 pages; v2: 46 pages, comments added, matches published version

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Cited by in corpus (21)

• Integrable Deformations of Sigma Models
• 4-dimensional Chern-Simons theory and integrable field theories
• Integrable $\mathcal{E}$-Models, 4d Chern-Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects
• RG flows of integrable $\sigma$-models and the twist function
• RG flow of integrable $\mathcal{E}$-models
• The Faddeev-Reshetikhin model from a 4D Chern-Simons theory
• Integrable degenerate $\mathcal{E}$-models from 4d Chern-Simons theory
• Homogeneous Yang-Baxter deformations as undeformed yet twisted models
• Universal 1-loop divergences for integrable sigma models
• On strong integrability of the dressing cosets
• Non-Abelian Toda field theories from a 4D Chern-Simons theory
• Yang-Baxter deformations of WZW model on the Heisenberg Lie group
• Yang-Baxter deformation of WZW model based on Lie supergroups: The cases of $GL(1|1)$ and $(C^3+A)$
• Lax pairs for new ${\mathbb{Z}}_N$-symmetric coset $\sigma$-models and their Yang-Baxter deformations
• On some integrable deformations of the Wess-Zumino-Witten model
• Yang-Baxter deformations of the $GL(2,\mathbb{R})$ WZW model and non-Abelian T-duality
• On a class of conformal $\mathcal{E}$-models and their chiral Poisson algebras
• Yang-Baxter deformations of the OSP(1|2) WZW model
• More on (gauged) WZW models over low-dimensional Lie supergroups and their integrable deformations
• Supergravity solution-generating techniques and canonical transformations of $\sigma$-models from $O(D,D)$
• Point particle E-models