Supergravity backgrounds for deformations of AdS_n×Sⁿ supercoset string models

We consider type IIB supergravity backgrounds corresponding to the deformed AdS_n×Sⁿ×T^10-2n supercoset string models of the type constructed in arXiv:1309.5850 [2] which depend on one deformation parameter κ. In AdS₂×S² case we find that the deformed metric can be extended to a full supergravity solution with non-trivial dilaton, RR scalar and RR 5-form strength. The solution depends on a free parameter a that should be chosen as a particular function of κ to correspond to the deformed supercoset model. In AdS₃×S³ case the full solution supported by the dilaton, RR scalar and RR 3-form strength exists only in the two special cases, a=0 and a=1. We conjecture that there may be a more general one-parameter solution supported by several RR fields that for particular a=a(κ) corresponds to the supercoset model. In the most complicated deformed AdS₅×S⁵ case we were able to find only the expressions for the dilaton and the RR scalar. The full solution is likely to be supported by a combination of the 5-form and 3-form field strengths. We comment on the singularity structure of the resulting metric and exact dilaton field.