On classical q-deformations of integrable σ-models
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In this article, a procedure is developed for constructing deformations of integrable σ-models which are themselves classically integrably this article and the actions correspond to a deformation of the target space geometry and include a torsion term.Abstract:
A procedure is developed for constructing deformations of integrable σ-models which are themselves classically integrable. When applied to the principal chiral model on any compact Lie group F, one recovers the Yang-Baxter σ-model introduced a few years ago by C. Klimyc´ok. In the case of the symmetric space σ-model on F/G we obtain a new one-parameter family of integrable σ-models. The actions of these models correspond to a deformation of the target space geometry and include a torsion term. An interesting feature of the construction is the q-deformation of the symmetry corresponding to left multiplication in the original models, which becomes replaced by a classical q-deformed Poisson-Hopf algebra. Another noteworthy aspect of the deformation in the coset σ-model case is that it interpolates between a compact and a non-compact symmetric space. This is exemplified in the case of the SU(2)/U(1) coset σ-model which interpolates all the way to the SU(1,1)/U(1) coset σ-model.read more
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Jordanian deformations of the AdS_5xS^5 superstring
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S-matrix for strings on η-deformed AdS5 × S5
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S-matrix for strings on $\eta$-deformed AdS5 x S5
TL;DR: In this article, the bosonic part of the superstring sigma model Lagrangian was determined and the perturbative world-sheet scattering matrix of bosonic particles of the model was computed.
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Jordanian deformations of the AdS5 × S5 superstring
TL;DR: In this paper, Jordanian deformations of the AdS5 × S5 superstring action correspond to non-standard q-deformations, and the classical action and the Lax pair are constructed with a linear, twisted and extended R operator.
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Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
TL;DR: In this article, an integrable q-deformation of the AdS_5 x S^5 superstring action was proposed, which is a generalization of the one previously developed for deforming principal chiral and symmetric space sigma-models.
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TL;DR: In this article, the authors prove that the Yang-Baxter σ model can be considered as an integrable deformation of the principal chiral model, and they find an explicit one-to-one map that transforms every solution of the chiral models into a solution of a deformed model.