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On integrable deformations of superstring sigma models related to \(\mathrm{AdS}_n \times \mathrm{S}^n\) supercosets. (English) Zbl 1329.81317
Summary: We consider two integrable deformations of 2d sigma models on supercosets associated with \(\mathrm{AdS}_n \times \mathrm{S}^n\). The first, the “\(\eta\)-deformation” (based on the Yang-Baxter sigma model), is a one-parameter generalization of the standard superstring action on \(\mathrm{AdS}_n \times \mathrm{S}^n\), while the second, the “\(\lambda\)-deformation” (based on the deformed gauged WZW model), is a generalization of the non-abelian T-dual of the \(\mathrm{AdS}_n \times \mathrm{S}^n\) 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 \(\mathrm{AdS}_2 \times \mathrm{S}^2\) case we then explore the effect of this limit on the supergravity background associated with 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 \(\mathrm{S}^2\).

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
81T10 Model quantum field theories
81T20 Quantum field theory on curved space or space-time backgrounds
16T25 Yang-Baxter equations
14D15 Formal methods and deformations in algebraic geometry
83E50 Supergravity
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