One-Instanton Calculations in $N=2$ Supersymmetric $SU(N_c)$ Yang-Mills Theory

Abstract

We calculate the one-instanton contribution to the prepotential in $N=2$ supersymmetric $SU(N_c)$ Yang-Mills theory from the microscopic viewpoint. We find that the holomorphy argument simplifies the group integrations of the instanton configurations. For $N_c=3$, the result agrees with the exact solution.

16 pages. Some minor changes of the references and the form of the paper

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• Multi-Instanton Calculus in N=2 Supersymmetric Gauge Theory II: Coupling to Matter
• The ABCDEFG of Instantons and W-algebras
• The Effective Prepotential of N=2 Supersymmetric SO(N_c) and Sp(N_c) Gauge Theories
• The Renormalization Group Equation in N=2 Supersymmetric Gauge Theories
• Whitham Hierarchies, Instanton Corrections and Soft Supersymmetry Breaking in N=2 SU(N) Super Yang-Mills Theory
• Instanton Calculus and Nonperturbative Relations in N=2 Supersymmetric Gauge Theories
• Saddle point equations in Seiberg-Witten theory
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• The Instanton Hunter's Guide to Supersymmetric SU(N) Gauge Theories
• Multi-Instantons, Three-Dimensional Gauge Theory, and the Gauss-Bonnet-Chern Theorem
• Exact and microscopic one-instanton calculations in N=2 supersymmetric Yang-Mills theories
• Solving N=2 SYM by Reflection Symmetry of Quantum Vacua
• Calculating the Prepotential by Localization on the Moduli Space of Instantons
• Instanton corrections in N=2 supersymmetric theories with classical gauge groups and fundamental matter hypermultiplets
• Non-holomorphic terms in N=2 SUSY Wilsonian actions and RG equation
• Modular Invariance and Structure of the Exact Wilsonian Action of N=2 SYM
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• On the Picard-Fuchs Equations for Massive N=2 Seiberg-Witten Theories
• Seiberg--Witten Duality in Dijkgraaf--Vafa Theory
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• One-Instanton Test of a Seiberg-Witten Curve from M-theory: the Antisymmetric Representation of SU(N)
• One-instanton predictions for non-hyperelliptic curves derived from M-theory
• Uniqueness of the Seiberg-Witten Effective Lagrangian
• Elliptic models and M-theory
• Picard-Fuchs Equations and Prepotential in N=2 Supersymmetric G_{2} Yang-Mills Theory
• Prepotentials in N=2 Supersymmetric SU(3) YM-Theory with Massless Hypermultiplets
• N=2 SYM Action as a BRST Exact Term, Topological Yang Mills and Instantons
• Simple Calculation of Instanton Corrections in Massive N=2 SU(3) SYM
• One-Instanton Tests of the Exact Results in N=2 Supersymmetric QCD
• On Explicit Evaluations Around the Conformal Point in N=2 Supersymmetric Yang-Mills Theories
• A-D-E Singularity and Prepotentials in N=2 Supersymmetric Yang-Mills Theory
• Higher Derivative Terms in the Effective Action of N=2 SUSY QCD from Instantons
• Calculating Gluino Condensates in $\mathcal{N}=1$ SYM from Seiberg-Witten Curves
• Prepotential of $N=2$ Supersymmetric Yang-Mills Theories in the Weak Coupling Region
• Picard-Fuchs Equations and Whitham Hierarchy in N=2 Supersymmetric SU(r+1) Yang-Mills Theory
• Charges of dyons in N=2 supersymmetric gauge theory
• Akin $N=2$ SUSY Yang Mills Theories and Instanton Expansion
• On the Picard-Fuchs Equations of N=2 Supersymmetric E_6 Yang-Mills Theory
• Geometric Engineering of Seiberg-Witten Theories with Massive Hypermultiplets
• Instanton Calculus and SUSY Gauge Theories on ALE Manifolds
• One-Instanton Prepotentials from WDVV equations in N=2 Supersymmetric SU(4) Yang-Mills Theory
• Low Energy Effective Action in N=2 Yang-Mills as an Integrated Anomaly
• Renormalon's Contribution to Effective Couplings
• Gauge Zero-Modes on ALE Manifolds
• Direct Derivation of Scaling Relation of Prepotential in N=2 Supersymmetric G_2 Yang-Mills Theory