Calculating the Prepotential by Localization on the Moduli Space of Instantons

Abstract

We describe a new technique for calculating instanton effects in supersymmetric gauge theories applicable on the Higgs or Coulomb branches. In these situations the instantons are constrained and a potential is generated on the instanton moduli space. Due to existence of a nilpotent fermionic symmetry the resulting integral over the instanton moduli space localizes on the critical points of the potential. Using this technology we calculate the one- and two-instanton contributions to the prepotential of SU(N) gauge theory with N=2 supersymmetry and show how the localization approach yields the prediction extracted from the Seiberg-Witten curve. The technique appears to extend to arbitrary instanton number in a tractable way.

24 pages, JHEP.cls, more references and extra discussion on N_F=2N case

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Cited by in corpus (24)

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• Extended Seiberg-Witten Theory and Integrable Hierarchy
• Instanton calculus in R-R background and the topological string
• A note on instanton counting for N=2 gauge theories with classical gauge groups
• Instantons on Quivers and Orientifolds
• Instanton effects in N=1 brane models and the Kahler metric of twisted matter
• Instantons in N=2 magnetized D-brane worlds
• Five-dimensional Chern-Simons terms and Nekrasov's instanton counting
• Fluxed M5-instantons in F-theory
• Zero Modes and the Atiyah-Singer Index in Noncommutative Instantons
• On the Coulomb Branch of a Marginal Deformation of N=4 SUSY Yang-Mills
• Superlocalization formulas and supersymmetric Yang-Mills theories
• The Liouville Geometry of N=2 Instantons and the Moduli of Punctured Spheres
• Wilson Loops and Chiral Correlators on Squashed Spheres
• Propagators in Noncommutative Instantons
• Microscopic quantum superpotential in N=1 gauge theories
• Glueball operators and the microscopic approach to N=1 gauge theories
• N=2 Instanton Calculus In Closed String Background
• On the Chiral Ring of N=1 Supersymmetric Gauge Theories
• Geometric Engineering of Seiberg-Witten Theories with Massive Hypermultiplets
• (D)-instanton effects in magnetized brane worlds