Spacetimes for λ-deformations

We examine a recently proposed class of integrable deformations to two-dimensional conformal field theories. These ?-deformations interpolate between a WZW model and the non-Abelian T-dual of a Principal Chiral Model on a group G or, between a G/H gauged WZW model and the non-Abelian T-dual of the geometric coset G/H. ?-deformations have been conjectured to represent quantum group q-deformations for the case where the deformation parameter is a root of unity. In this work we show how such deformations can be given an embedding as full string backgrounds whose target spaces satisfy the equations of type-II supergravity. One illustrative example is a deformation of the Sl(2,?)/U(1) black-hole CFT. A further example interpolates between the SU(2)×SU(2)SU(2)×SL(2,?)×SL(2,?)SL(2,?)U(1)4 gauged WZW model and the non-Abelian T-dual of AdS 3 × S 3 × T 4 supported with Ramond flux.