Flat Coordinates, Topological Landau-Ginzburg Models and the Seiberg-Witten Period Integrals

TL;DR

This paper explores the connection between four-dimensional N=2 supersymmetric gauge theories and two-dimensional topological Landau-Ginzburg models through the study of Picard-Fuchs equations and Seiberg-Witten period integrals.

Contribution

It derives the Picard-Fuchs equations for A-D-E gauge groups using flat coordinates and shows their equivalence to the Gauss-Manin system in topological Landau-Ginzburg models, revealing a new relationship.

Findings

Picard-Fuchs equations for A-D-E gauge groups derived.

Equivalence established between Picard-Fuchs system and Gauss-Manin system.

Identified relationship between 4D N=2 gauge theories and 2D topological field theories.

Abstract

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.