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Supergravity background of lambda-deformed model for AdS2 x S2 supercoset

Starting with the F/G supercoset model corresponding to the AdS_n x S^n superstring one can define the lambda-model of arXiv:1409.1538 either as a deformation of the F/F gauged WZW model or as an integrable one-parameter generalization of the non-abelian T-dual of the AdS_n x S^n superstring sigma model with respect to the whole supergroup F. Here we consider the case of n=2 and find the explicit form of the 4d target space background for the lambda-model for the PSU(1,1|2)/[SO(1,1) x SO(2)] supercoset. We show that this background represents a solution of type IIB 10d supergravity compactified on a 6-torus with only metric, dilaton Phi and the RR 5-form (represented by a 2-form F in 4d) being non-trivial. This implies that the lambda-model is Weyl invariant at the quantum level and thus defines a consistent superstring sigma model. The supergravity solution we find is different from the one in arXiv:1410.1886 which should correspond to a version of the lambda-model where only the bosonic subgroup of F is gauged. Still, the two solutions have equivalent scaling limit of arXiv:1504.07213 leading to the isometric background for the metric and e^Phi F which is related to the eta-deformed AdS_2 x S^2 sigma model of arXiv:1309.5850. Similar results are expected in the AdS_3 x S^3 and AdS_5 x S^5 cases.