On integrable deformations of superstring sigma models related to AdS_n x S^n supercosets

Abstract

We consider two integrable deformations of 2d sigma models on supercosets associated with AdS_n x S^n. The first, the "eta-deformation" (based on the Yang-Baxter sigma model), is a one-parameter generalization of the standard superstring action on AdS_n x S^n, while the second, the "lambda-deformation" (based on the deformed gauged WZW model), is a generalization of the non-abelian T-dual of the AdS_n x S^n superstring. We show that the eta-deformed model may be obtained from the lambda-deformed one by a special scaling limit and analytic continuation in coordinates combined with a particular identification of the parameters of the two models. The relation between the couplings and deformation parameters is consistent with the interpretation of the first model as a real quantum deformation and the second as a root of unity quantum deformation. For the AdS_2 x S^2 case we then explore the effect of this limit on the supergravity background associated to the lambda-deformed model. We also suggest that the two models may form a dual Poisson-Lie pair and provide direct evidence for this in the case of the integrable deformations of the coset associated with S^2.

v2: comments and references added; v3: new appendix on an alternative proposal for the dilaton and minor changes, 28 pages; v4: misprint in (B.7) corrected

References in corpus (16)

• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• On deformations of AdS_n x S^n supercosets
• An Integrable Deformation of the AdS5 x S5 Superstring
• Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model
• Quantum Deformations of the One-Dimensional Hubbard Model
• Deformed integrable $\sigma$-models, classical $R$-matrices and classical exchange algebra on Drinfel'd doubles
• Integrable Deformations of Strings on Symmetric Spaces
• Spacetimes for λ-deformations
• Towards a two-parameter q-deformation of AdS_3 x S^3 x M^4 superstrings
• On the exact spectrum and mirror duality of the (AdS_5 x S^5)_eta superstring
• The ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ mirror model as a string
• On reduced models for superstrings on AdS_n x S^n
• Double Wick rotating Green-Schwarz strings
• Sine-Gordon-like action for the Superstring in AdS(5) x S(5)
• Integrable $\lambda$-deformations: Squashing Coset CFTs and $Ad{S}_5\times S^5$

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