Renormalisability of non-homogeneous T-dualised sigma-models

The quantum equivalence between σ-models and their non-Abelian T-dualised partners is examined for a large class of four dimensional non-homogeneous and quasi-Einstein metrics with an isometry group SU(2)×U(1). We prove that the one-loop renormalisability of the initial torsionless σ-models is equivalent to the one-loop renormalisability of the T-dualised torsionful model. For a subclass of Kähler original metrics, the dual partners are still Kähler (with torsion).