Alleviating the non-ultralocality of coset sigma models through a generalized Faddeev-Reshetikhin procedure

Abstract

The Faddeev-Reshetikhin procedure corresponds to a removal of the non-ultralocality of the classical SU(2) principal chiral model. It is realized by defining another field theory, which has the same Lax pair and equations of motion but a different Poisson structure and Hamiltonian. Following earlier work of M. Semenov-Tian-Shansky and A. Sevostyanov, we show how it is possible to alleviate in a similar way the non-ultralocality of symmetric space sigma models. The equivalence of the equations of motion holds only at the level of the Pohlmeyer reduction of these models, which corresponds to symmetric space sine-Gordon models. This work therefore shows indirectly that symmetric space sine-Gordon models, defined by a gauged Wess-Zumino-Witten action with an integrable potential, have a mild non-ultralocality. The first step needed to construct an integrable discretization of these models is performed by determining the discrete analogue of the Poisson algebra of their Lax matrices.

31 pages; v2: minor changes

References in corpus (6)

• Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model
• Pohlmeyer reduction revisited
• The classical R-matrix of AdS/CFT and its Lie dialgebra structure
• The Classical Exchange Algebra of AdS5 x S5 String Theory
• On the perturbative S-matrix of generalized sine-Gordon models
• Supersymmetry Flows, Semi-Symmetric Space Sine-Gordon Models And The Pohlmeyer Reduction

Cited by in corpus (29)

• 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
• Integrable Deformations of Strings on Symmetric Spaces
• On the Hamiltonian integrability of the bi-Yang-Baxter sigma-model
• Exotic symmetry and monodromy equivalence in Schrodinger sigma models
• S-Matrices and Quantum Group Symmetry of k-Deformed Sigma Models
• Alleviating the non-ultralocality of the AdS_5 x S^5 superstring
• Local charges in involution and hierarchies in integrable sigma-models
• Homogeneous Yang-Baxter deformations as undeformed yet twisted models
• Integrable Lambda Models And Chern-Simons Theories
• Quantum Inverse Scattering and the Lambda Deformed Principal Chiral Model
• Quantum Anisotropic Sigma and Lambda Models as Spin Chains
• On the quantization of continuous non-ultralocal integrable systems
• Semiclassical spectrum of a Jordanian deformation of $Ad{S}_5\times S^5$
• Lambda Models From Chern-Simons Theories
• The Structure of Non-Abelian Kinks
• On the equivalence theorem for integrable systems
• Symplectic Deformations of Integrable Field Theories and AdS/CFT
• On strong integrability of the dressing cosets
• Integrable theories and generalized graded Maillet algebras
• Deformed WZW Models and Hodge Theory -- Part I
• The r-matrix of the Alday-Arutyunov-Frolov model
• Integrability of D1-brane on Group Manifold with Mixed Three Form Flux
• Integrability of D1-brane on Group Manifold
• Generalized sine-Gordon models and quantum braided groups
• Algebraic structure of classical integrability for complex sine-Gordon
• Towards a quadratic Poisson algebra for the subtracted classical monodromy of Symmetric Space Sine-Gordon theories
• Integrable models from 4d holomorphic BF theory