Gauged linear sigma-models and Calabi-Yau spaces

The talk is devoted to two-dimensional supersymmetric field theories with gauge fields. E.Witten noted that depending on the sign of the coupling constant in a twisted superpotential and the choice of interacting fields with a gauge field, different spaces of classical solutions are obtained. In one limit, the Landau-Ginzburg orbifolds are obtained, and in another limit there are Calabi-Yau spaces. We will discuss some examples.