Localization principle in SUSY gauge theories

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.

21 pages, a review article to appear in PTEP Special Section "Structure of supersymmetric gauge theories"

References in corpus (14)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Notes on SUSY Gauge Theories on Three-Sphere
• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• Supersymmetric Gauge Theories on the Five-Sphere
• AGT on the S-duality Wall
• Seiberg-Witten prepotential from instanton counting
• A review of the T_N theory and its cousins
• Exact Instanton Expansion of ABJM Partition Function
• Chern-Simons Theory and S-duality
• From Liouville Theory to the Quantum Geometry of Riemann Surfaces
• A review on SUSY gauge theories on $S^3$
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Index calculation by means of harmonic expansion

Cited by in corpus (9)

• The star-triangle relation, lens partition function, and hypergeometric sum/integrals
• Exact Instanton Expansion of ABJM Partition Function
• Twisting and localization in supergravity: equivariant cohomology of BPS black holes
• Killing-Yano tensor and supersymmetry of the self-dual Plebanski-Demianski solution
• Multi-cut Solutions in Chern-Simons Matrix Models
• Exact solution of Chern-Simons-matter matrix models with characteristic/orthogonal polynomials
• Mordell integrals and Giveon-Kutasov duality
• Pentagon identities arising in supersymmetric gauge theory computations
• Localization of four-dimensional super Yang-Mills theories compactified on Riemann surface