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2015•Progress of Theoretical and Experimental PhysicsOpen access

The localization principle in SUSY gauge theories

Kazuo Hosomichi

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Abstract

The 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 |${\mathcal N}=2$| supersymmetric gauge theories on |$S^4$| and the subsequent developments on three- or four-dimensional gauge theories on spheres.

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The 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 |${\mathcal N}=2$| supersymmetric gauge theories on |$S^4$| and the subsequent developments on three- or four-dimensional gauge theories on spheres.

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Available abstract

The 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 |${\mathcal N}=2$| supersymmetric gauge theories on |$S^4$| and the subsequent developments on three- or four-dimensional gauge theories on spheres.

Key concepts: Physics, Supersymmetric gauge theory, Supersymmetry, Gauge theory, Gauge (firearms), Theoretical physics, Hamiltonian lattice gauge theory, Introduction to gauge theory

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