The Exact Low Energy Effective action of $\mathcal{N}=2$ SYM via Seiberg-Witten Theory and Localisation

Abstract

In the mid 1990's Seiberg and Witten determined the exact low energy effective action of $\mathcal{N}=2$ supersymmetric Yang-Mills theory with gauge group $SU(2)$. Later, in the early 2000's Nekrasov calculated this action directly using localisation techniques. This work serves as an introduction to the area, developing both approaches and reconciling their results.