Localization principle in SUSY gauge theories

TL;DR

This paper reviews the localization principle in supersymmetric gauge theories, highlighting its role in enabling explicit path integral calculations and its impact on understanding strong coupling dynamics and M-theory branes.

Contribution

It summarizes key developments in localization techniques, especially Pestun's solution for 4D N=2 theories on S^4 and recent advances in lower-dimensional gauge theories.

Findings

Explicit formulas for supersymmetric path integrals

Insights into strong coupling behavior of gauge theories

Advances in gauge theories on spheres

Abstract

Localization principle is a powerful analytic tool in supersymmetric gauge theories which enables one to perform supersymmetric path integrals explicitly. Many important formulae have been obtained, and they led to a major breakthrough in the understanding of gauge theories at strong coupling as well as the dynamics of branes in M-theory. Some of those results are reviewed, focusing especially on Pestun's solution to four-dimensional N=2 supersymmetric gauge theories on S^4 and the subsequent developments on three or four-dimensional gauge theories on spheres.