Affine q-deformed symmetry and the classical Yang-Baxter sigma-model

Abstract

The Yang-Baxter $\sigma$-model is an integrable deformation of the principal chiral model on a Lie group $G$. The deformation breaks the $G\times G$ symmetry to $U(1{)}^{\text{rank}(G)}\times G$. It is known that there exist non-local conserved charges which, together with the unbroken $U(1{)}^{\text{rank}(G)}$ local charges, form a Poisson algebra ${\mathcal{U}}_q(\mathfrak{g})$, which is the semiclassical limit of the quantum group $U_q(\mathfrak{g})$, with $\mathfrak{g}$ the Lie algebra of $G$. For a general Lie group $G$ with rank$(G)>1$, we extend the previous result by constructing local and non-local conserved charges satisfying all the defining relations of the infinite-dimensional Poisson algebra ${\mathcal{U}}_q(L\mathfrak{g})$, the classical analogue of the quantum loop algebra $U_q(L\mathfrak{g})$, where $L\mathfrak{g}$ is the loop algebra of $\mathfrak{g}$. Quite unexpectedly, these defining relations are proved without encountering any ambiguity related to the non-ultralocality of this integrable $\sigma$-model.

21 pages, references added

References in corpus (9)

• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• An Integrable Deformation of the AdS5 x S5 Superstring
• Integrable Deformations of Strings on Symmetric Spaces
• Towards a two-parameter q-deformation of AdS_3 x S^3 x M^4 superstrings
• Yangian symmetry in deformed WZNW models on squashed spheres
• Hidden Yangian symmetry in sigma model on squashed sphere
• Classical Integrability of the Squashed Three-sphere, Warped AdS3 and Schroedinger Spacetime via T-Duality
• The classical Yang-Baxter equation and the associated Yangian symmetry of gauged WZW-type theories
• Anisotropic Landau-Lifshitz sigma models from q-deformed AdS_5 x S^5 superstrings

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• Deformations of the Almheiri-Polchinski model
• Classical and Quantum Aspects of Yang-Baxter Wess-Zumino Models
• Local charges in involution and hierarchies in integrable sigma-models
• Integrable deformations of coupled sigma-models
• Integrable Lambda Models And Chern-Simons Theories
• On Yang-Baxter models, twist operators, and boundary conditions
• Yang Baxter and Anisotropic Sigma and Lambda Models, Cyclic RG and Exact S-Matrices
• Probing analytical and numerical integrability: The curious case of $(Ad{S}_5\times S^5{)}_{\eta }$
• An elliptic integrable deformation of the Principal Chiral Model