  We study gauged linear sigma models for noncompact Calabi-Yau manifolds
described as a line bundle on a hypersurface in a projective space. This gauge
theory has a unique phase if the Fayet-Iliopoulos parameter is positive, while
there exist two distinct phases if the parameter is negative. We find four
massless effective theories in the infrared limit, which are related to each
other under the Calabi-Yau/Landau-Ginzburg correspondence and the topology
change. In the T-dual theory, on the other hand, we obtain two types of exact
massless effective theories: One is the sigma model on a newly obtained
Calabi-Yau geometry as a mirror dual, while the other is given by a
Landau-Ginzburg theory with a negative power term, indicating N=2
superconformal field theory on SL(2,R)/U(1). We argue that the effective
theories in the original gauged linear sigma model are exactly realized as N=2
Liouville theories coupled to well-defined Landau-Ginzburg minimal models.
