Construction of supergravity backgrounds with a dilaton field

A new class of non-compact Kähler backgrounds accompanied by a non-constant dilaton field is constructed as a supergravity solution. It is interpreted as a complex line bundle over a base manifold comprising of a combination of arbitrary coset spaces, and also includes the case of Calabi-Yau manifolds. The resulting backgrounds have U(1) isometry. We consider N=2 supersymmetric σ-models on them, and derive a non-Kählerian solution by U(1) duality transformation, which preserves N=2 supersymmetry.