Construction of supersymmetric nonlinear sigma models on noncompact Calabi-Yau manifolds with isometry

We propose a class of script N sign = 2 supersymmetric nonlinear sigma models on the noncompact Ricci-flat Kähler manifolds, interpreted as the complex line bundles over the hermitian symmetric spaces. Kähler potentials and Ricci-flat metrics for these manifolds with isometries are explicitly constructed by using the techniques of supersymmetric gauge theories. Each of the metrics contains a resolution parameter which controls the size of these base manifolds, and the conical singularity appears when the parameter vanishes.