It is therefore natural to conjecture that taking an appropriate limit in the λ-model associated with the AdS5×S5 superset will give the deformed model whose light-cone gauge S-matrix is that of . An important feature of the special limit is that it generates isometries. However, as the λ-model has no isometries one cannot fix the associated light-cone gauge and hence there is no apparent connection to the S-matrix of . For q equal a phase, unitarity can be restored , and the resulting S-matrix has been conjectured to be related to the λ-model , . For q real, the S-matrix is unitary and has been shown to be in perturbative agreement , with the η-model of . This special limit is of particular interest for understanding the relation of the λ-model to the q-deformation of the light-cone gauge S-matrix for q being a phase. This provides, therefore, a direct link between the special limit of the λ-model and the PR model (conjectured in , and recently made explicit in ). 2 The special point ϰ=i of the η-model is a pp-wave background that for low-dimensional examples is equivalent in the light-cone gauge to the Pohlmeyer-reduced (PR) model for the coset theory. Superstring 3.3.4 Crack:Īt the same time, it turns out there is also another, more surprising, relation: the η-model can be obtained directly from the λ-model as a special limit (combined with an analytic continuation), which in some sense cuts off the asymptotically flat region. 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 cost associated with. For the case we then explore the effect of this limit on the supergravity background associated with the λ-deformed model. 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. 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. We consider two integrable deformations of 2d sigma models on supersets associated with. The first, the “ η-deformation” (based on the Yang–Baxter sigma model), is a one-parameter generalization of the standard superstring action on, while the second, the “ λ-deformation” (based on the deformed gauged WZW model), is a generalization of the non-abelian T-dual of the superstring.
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