Duality in N=2 SUSY SU(2) Yang-Mills Theory: A pedagogical introduction to the work of Seiberg and Witten

TL;DR

This paper provides a detailed, pedagogical overview of Seiberg and Witten's groundbreaking work on N=2 supersymmetric SU(2) gauge theory, focusing on duality, monodromies, and effective actions without relying heavily on elliptic curves.

Contribution

It offers an accessible introduction to Seiberg and Witten's methods, emphasizing the relation between monodromies and differential equations in the low-energy effective theory.

Findings

Clarification of duality in N=2 SUSY SU(2) Yang-Mills

Connection between monodromies and differential equations

Pedagogical derivation of low-energy effective action

Abstract

These are notes from introductory lectures given at the Ecole Normale in Paris and at the Strasbourg meeting dedicated to the memory of Claude Itzykson. I review in considerable detail and in a hopefully pedagogical way the work of Seiberg and Witten on $N=2$ supersymmetric $SU(2)$ gauge theory without extra matter. This presentation basically follows their original work, except in the last section where the low-energy effective action is obtained emphasizing more the relation between monodromies and differential equations rather than using elliptic curves.