On the classical equivalence of monodromy matrices in squashed sigma model

Abstract

We proceed to study the hybrid integrable structure in two-dimensional non-linear sigma models with target space three-dimensional squashed spheres. A quantum affine algebra and a pair of Yangian algebras are realized in the sigma models and, according to them, there are two descriptions to describe the classical dynamics 1) the trigonometric description and 2) the rational description, respectively. For every description, a Lax pair is constructed and the associated monodromy matrix is also constructed. In this paper we show the gauge-equivalence of the monodromy matrices in the trigonometric and rational description under a certain relation between spectral parameters and the rescalings of sl(2) generators.

32pages, 3figures, references added, introduction and discussion sections revised

References in corpus (7)

• Warped AdS3/Dipole-CFT Duality
• q-Deformation of the AdS5 x S5 Superstring S-matrix and its Relativistic Limit
• Yangian symmetry in deformed WZNW models on squashed spheres
• The classical origin of quantum affine algebra in squashed sigma models
• Hidden Yangian symmetry in sigma model on squashed sphere
• Classical integrability of Schrodinger sigma models and q-deformed Poincare symmetry
• Hybrid classical integrable structure of squashed sigma models -- a short summary

Cited by in corpus (42)

• An integrable deformation of the AdS_5 x S^5 superstring action
• On classical q-deformations of integrable sigma-models
• 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
• Jordanian deformations of the AdS_5xS^5 superstring
• Integrability of the bi-Yang-Baxter sigma-model
• Lunin-Maldacena backgrounds from the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence
• Yang-Baxter sigma models based on the CYBE
• Integrability of classical strings dual for noncommutative gauge theories
• On the exact spectrum and mirror duality of the (AdS_5 x S^5)_eta superstring
• Integrable double deformation of the principal chiral model
• A Jordanian deformation of AdS space in type IIB supergravity
• Schrödinger geometries arising from Yang-Baxter deformations
• A new coordinate system for q-deformed AdS_5 x S^5 and classical string solutions
• Schrodinger Sigma Models and Jordanian Twists
• A deformation of quantum affine algebra in squashed WZNW models
• Assembling integrable sigma-models as affine Gaudin models
• Deformed Neumann model from spinning strings on (AdS_5 x S^5)_η
• Generalized type IIB supergravity equations and non-Abelian classical r-matrices
• 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
• 4-dimensional Chern-Simons theory and integrable field theories
• Exotic symmetry and monodromy equivalence in Schrodinger sigma models
• S-Matrices and Quantum Group Symmetry of k-Deformed Sigma Models
• Yang-Baxter sigma models: Quantum aspects
• Deformations of the Almheiri-Polchinski model
• Classical and Quantum Aspects of Yang-Baxter Wess-Zumino Models
• Dressing cosets and multi-parametric integrable deformations
• Anisotropic Landau-Lifshitz sigma models from q-deformed AdS_5 x S^5 superstrings
• String theories on warped AdS backgrounds and integrable deformations of spin chains
• Local charges in involution and hierarchies in integrable sigma-models
• Affine q-deformed symmetry and the classical Yang-Baxter sigma-model
• Integrable deformations of coupled sigma-models
• On q-deformed symmetries as Poisson-Lie symmetries and application to Yang-Baxter type models
• Deformed Integrable Models from Holomorphic Chern-Simons Theory
• $O(d,d)$ transformations preserve classical integrability
• Yang Baxter and Anisotropic Sigma and Lambda Models, Cyclic RG and Exact S-Matrices
• Yang-Baxter sigma models and Lax pairs arising from $\kappa$-Poincaré $r$-matrices
• Finite-size effect of η-deformed AdS_5 x S^5 at strong coupling
• An elliptic integrable deformation of the Principal Chiral Model
• Constrained affine Gaudin models and diagonal Yang-Baxter deformations
• Generalized quark-antiquark potentials from a $q$-deformed AdS${}_5\times$S${}^5$ background