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

Starting with the (F) over cap /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) over cap/(F) over cap gauged WZW model or as an integrable one-parameter generalisationof the non-abelian T-dual of the AdS(n) x S-n superstring sigma model with respect to the whole supergroup (F) over cap. 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 vertical bar 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 Fin 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) over cap 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. (C) 2016 The Authors. Published by Elsevier B.V.