Flat coordinates, topological Landau-Ginzburg models and the Seiberg-Witten period integrals

We study the Picard-Fuchs differential equations for the Seiberg-Witten period integrals in N = 2 supersymmetric Yang-Mills theory. For A-D-E gauge groups we derive the Picard-Fuchs equations by using the flat coordinates in the A-D-E singularity theory. We then find that these are equivalent to the Gauss-Manin system for two-dimensional A-D-E topological Landau-Ginzburg models and the scaling relation for the Seiberg-Witten differential. This suggests an interesting relationship between four-dimensional N = 2 gauge theories in the Coulomb branch and two-dimensional topological field theories.