Type IIB supergravity solution for the T-dual of the η-deformed AdS₅×S⁵ superstring

We find an exact type IIB supergravity solution that represents a one-parameter deformation of the T-dual of the AdS₅×S⁵ background (with T-duality applied in all 6 abelian bosonic isometric directions). The non-trivial fields are the metric, dilaton and RR 5-form only. The latter has remarkably simple "undeformed" form when written in terms of a "deformation-rotated" vielbein basis. An unusual feature of this solution is that the dilaton contains a linear dependence on the isometric coordinates of the metric precluding a straightforward reversal of T-duality. If we still formally dualize back, we find exactly the metric, B-field and product of dilaton with RR field strengths as recently extracted from the η-deformed AdS₅×S⁵ superstring action in http://arxiv.org/abs/1507.04239. We also discuss similar solutions for deformed AdS_n×Sⁿ backgrounds with n=2,3. In the η→i limit we demonstrate that all these backgrounds can be interpreted as special limits of gauged WZW models and are also related to (a limit of) the Pohlmeyer-reduced models of the AdS_n×Sⁿ superstrings.