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

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