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

Starting with the Fˆ/G supercoset model corresponding to the AdSn×SnAdSn×Sn superstring one can define the λ-model of arXiv:1409.1538 either as a deformation of the Fˆ/Fˆ gauged WZW model or as an integrable one-parameter generalisation of the non-abelian T-dual of the AdSn×SnAdSn×Sn superstring sigma model with respect to the whole supergroup Fˆ. Here we consider the case of n=2n=2 and find the explicit form of the 4d target space background for the λ  -model for the PSU(1,1|2)/SO(1,1)×SO(2)PSU(1,1|2)/SO(1,1)×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 Φ and the RR 5-form (represented by a 2-form F in 4d) being non-trivial. This implies that the λ-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 λ  -model where only the bosonic subgroup of Fˆ is gauged. Still, the two solutions have equivalent scaling limit of arXiv:1504.07213 leading to the isometric background for the metric and eΦFeΦF which is related to the η  -deformed AdS2×S2AdS2×S2 sigma model of arXiv:1309.5850. Similar results are expected in the AdS3×S3AdS3×S3 and AdS5×S5AdS5×S5 cases.