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.

arXiv comment45 pages; v2: 46 pages, comments added, matches published version

References in corpus (50)

• On integrability of the Yang-Baxter $\si$-model
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• On classical q-deformations of integrable sigma-models
• Poisson-Lie T-duality and Loop Groups of Drinfeld Doubles
• Integrability and the AdS(3)/CFT(2) correspondence
• On deformations of AdS_n x S^n supercosets
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• Integrability of the bi-Yang-Baxter sigma-model
• Deformed integrable $\sigma$-models, classical $R$-matrices and classical exchange algebra on Drinfel'd doubles
• B-field in AdS(3)/CFT(2) Correspondence and Integrability
• Abelian Yang-Baxter Deformations and TsT transformations
• Lunin-Maldacena backgrounds from the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence
• Gauge Theory and Integrability, II
• Extended jordanian twists for Lie algebras
• Gauge Theory and Integrability, I
• Integrable deformations of T-dual $\sigma$ models
• Towards a two-parameter q-deformation of AdS_3 x S^3 x M^4 superstrings
• Supersymmetric gauge theory and the Yangian
• Integrable double deformation of the principal chiral model
• Yangian symmetry in deformed WZNW models on squashed spheres
• Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS_5 sigma-model
• Almost abelian twists and AdS/CFT
• Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings
• The integrable harmonic map problem versus Ricci flow
• On non-abelian T-duality and deformations of supercoset string sigma-models
• Non-Abelian Momentum-Winding Exchange
• The classical R-matrix of AdS/CFT and its Lie dialgebra structure
• A unifying 2d action for integrable $\sigma$-models from 4d Chern-Simons theory
• Chains of twists for classical Lie algebras
• A deformation of quantum affine algebra in squashed WZNW models
• Assembling integrable sigma-models as affine Gaudin models
• Gauge Theory And Integrability, III
• Yang-Baxter $\sigma$-model with WZNW term as $\mathcal{E}$-model
• Combining the bi-Yang-Baxter deformation, the Wess-Zumino term and TsT transformations in one integrable sigma-model
• On the Hamiltonian integrability of the bi-Yang-Baxter sigma-model
• Integrable coupled sigma-models
• Marginal deformations of WZW models and the classical Yang-Baxter equation
• Dressing cosets and multi-parametric integrable deformations
• Classical and Quantum Aspects of Yang-Baxter Wess-Zumino Models
• Comments on $\eta$-deformed principal chiral model from 4D Chern-Simons theory
• Local charges in involution and hierarchies in integrable sigma-models
• Three-parameter integrable deformation of Z_4 permutation supercosets
• Integrable deformations of coupled sigma-models
• Sigma models with local couplings: a new integrability -- RG flow connection
• The classical r-matrix method for nonlinear sigma-model
• Integrable models with twist function and affine Gaudin models
• Strong integrability of the bi-YB-WZ model
• On integrability of 2-dimensional $\sigma$-models of Poisson-Lie type
• Chains of extended Jordanian twists for Lie superalgebras
• Homotopical analysis of 4d Chern-Simons theory and integrable field theories

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