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

TL;DR

This paper reviews and reconciles two approaches—Seiberg-Witten theory and localization techniques—to determine the exact low energy effective action of $ ext{SU}(2)$ $ ext{N}=2$ supersymmetric Yang-Mills theory, highlighting their consistency.

Contribution

It provides a comprehensive introduction that develops both Seiberg-Witten and localization methods and demonstrates their agreement in computing the effective action.

Findings

Seiberg-Witten theory yields the exact low energy effective action.

Localization techniques confirm the Seiberg-Witten results.

The two approaches are shown to be consistent and complementary.

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.