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

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.

arXiv comment33 pages, uses PHYZZX

References in corpus (7)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Simple Singularities and N=2 Supersymmetric Yang-Mills Theory
• The Vacuum Structure and Spectrum of N=2 Supersymmetric SU(N) Gauge Theory
• Dyon - Monopole Bound States, Self-Dual Harmonic Forms on the Multi-Monopole Moduli Space, and SL(2,Z) Invariance in String Theory
• Electric-Magnetic Duality and Effective Field Theories
• Recent Results in String Duality
• Black Hole Condensation and Duality in String Theory

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