On integrable deformations of superstring sigma models related to AdSn×Sn supercosets

Abstract

We consider two integrable deformations of 2d sigma models on supercosets associated with AdSn×Sn. The first, the “η-deformation” (based on the Yang–Baxter sigma model), is a one-parameter generalization of the standard superstring action on AdSn×Sn, while the second, the “λ-deformation” (based on the deformed gauged WZW model), is a generalization of the non-abelian T-dual of the AdSn×Sn superstring. We show that the η-deformed model may be obtained from the λ-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 AdS2×S2 case we then explore the effect of this limit on the supergravity background associated with the λ-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 S2.