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.

arXiv comment1+32 pages, Latex, v2: few minor changes, NPB version, v3: A factor of two corrected in (A.22)

References in corpus (24)

• On integrability of the Yang-Baxter $\si$-model
• An integrable deformation of the AdS_5 x S^5 superstring action
• Duality Symmetries from Non--Abelian Isometries in String Theories
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• On classical q-deformations of integrable sigma-models
• Integrable interpolations: From exact CFTs to non-Abelian T-duals
• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• S-matrix for strings on $\eta$-deformed AdS5 x S5
• On non-abelian T-dual geometries with Ramond fluxes
• Currents, Charges, and Canonical Structure of Pseudodual Chiral Models
• Introduction to Yangian symmetry in integrable field theory
• Non-Abelian T-duality and the AdS/CFT correspondence:new N=1 backgrounds
• An Introduction to Yangian Symmetries
• Non-Abelian Duality and Canonical Transformations
• Hints of 5d Fixed Point Theories from Non-Abelian T-duality
• The all-loop non-Abelian Thirring model and its RG flow
• Yangian symmetry in deformed WZNW models on squashed spheres
• A new family of $SU(2)$ symmetric integrable sigma models
• Gauged WZW-type theories and the all-loop anisotropic non-Abelian Thirring model
• Non--Abelian Duality, Parafermions and Supersymmetry
• A deformation of quantum affine algebra in squashed WZNW models
• G-structures and Flavouring non-Abelian T-duality
• Integrable theories that are asymptotically CFT
• On the geometry of classically integrable two-dimensional non-linear sigma models

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