Gauge Theoretical Construction of Non-compact Calabi-Yau Manifolds

Abstract

We construct the non-compact Calabi-Yau manifolds interpreted as the complex line bundles over the Hermitian symmetric spaces. These manifolds are the various generalizations of the complex line bundle over CP^{N-1}. Imposing an F-term constraint on the line bundle over CP^{N-1}, we obtain the line bundle over the complex quadric surface Q^{N-2}. On the other hand, when we promote the U(1) gauge symmetry in CP^{N-1} to the non-abelian gauge group U(M), the line bundle over the Grassmann manifold is obtained. We construct the non-compact Calabi-Yau manifolds with isometries of exceptional groups, which we have not discussed in the previous papers. Each of these manifolds contains the resolution parameter which controls the size of the base manifold, and the conical singularity appears when the parameter vanishes.