Solving N=2 SYM by Reflection Symmetry of Quantum Vacua

Abstract

The recently rigorously proved nonperturbative relation between u and the prepotential, underlying N=2 SYM with gauge group SU(2), implies both the reflection symmetry $\overline{u(\tau )}=u(-\bar{\tau })$ and $u(\tau +1)=-u(\tau )$ which hold exactly. The relation also implies that $\tau$ is the inverse of the uniformizing coordinate u of the moduli space of quantum vacua. In this context, the above quantum symmetries are the key points to determine the structure of the moduli space. It turns out that the functions a(u) and a_D(u), which we derive from first principles, actually coincide with the solution proposed by Seiberg and Witten. We also consider some relevant generalizations.

12 pg. LaTex, Discussion of the generalization to higher rank groups added. To be published in Phys. Rev. D

References in corpus (17)

• The Strong-Coupling Spectrum of the Seiberg-Witten Theory
• Multi-Instanton Calculus in $N=2$ Supersymmetric Gauge Theory
• WDVV-like equations in N=2 SUSY Yang-Mills Theory
• Large Softly broken N=2 QCD
• One-Instanton Calculations in $N=2$ Supersymmetric $SU(N_c)$ Yang-Mills Theory
• Nonperturbative Renormalization Group Equation and Beta Function in N=2 SUSY Yang-Mills
• Superconformal Ward Identities and N=2 Yang-Mills Theory
• Multi-Instanton Check of the Relation Between the Prepotential F and the Modulus u in N=2 SUSY Yang-Mills Theory
• Instanton Calculus and Nonperturbative Relations in N=2 Supersymmetric Gauge Theories
• Nonperturbative Relations in N=2 SUSY Yang-Mills and WDVV equation
• Phase Transitions in Softly Broken N=2 SQCD at Non-zero Theta Angle
• Instanton-induced Effective Lagrangian in the Seiberg-Witten Model
• Multi-instanton calculus in N=2 supersymmetric QCD
• On the Moduli Space of N = 2 Supersymmetric G_2 Gauge Theory
• Multi-instanton calculus versus exact results in N=2 supersymmetric QCD
• Charge fractionization in N=2 supersymmetric QCD
• Mass, Confinement and CP Invariance in the Seiberg-Witten Model"

Cited by in corpus (26)

• On N=2 Supersymmetric QCD with 4 Flavors
• Partial Breaking of N=2 Supersymmetry and of Gauge Symmetry in the U(N) Gauge Model
• Non-holomorphic terms in N=2 SUSY Wilsonian actions and RG equation
• Supersymmetric U(N) Gauge Model and Partial Breaking of N=2 Supersymmetry
• The dyon spectra of finite gauge theories
• Seiberg--Witten Duality in Dijkgraaf--Vafa Theory
• Branched Matrix Models and the Scales of Supersymmetric Gauge Theories
• On The Beta-Function in N=2 Supersymmetric Yang-Mills Theory
• N=2 SYM RG Scale as Modulus for WDVV Equations
• Picard-Fuchs Equation and Prepotential of Five Dimensional SUSY Gauge Theory Compactified on a Circle
• Integrability, Seiberg-Witten Models and Picard-Fuchs Equations
• The Liouville Geometry of N=2 Instantons and the Moduli of Punctured Spheres
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Beta Function, C--Theorem and WDVV Equations in 4D N=2 SYM
• On the WDVV Equation and M-Theory
• Multi-Instanton Measure from Recursion Relations in N=2 Supersymmetric Yang-Mills Theory
• Supersymmetry Breaking Vacua from M Theory Fivebranes
• The Instanton Universal Moduli Space of N=2 Supersymmetric Yang-Mills Theory
• Modular Invariant Regularization of String Determinants and the Serre GAGA Principle
• SU(2) Yang-Mills Theory with extended Supersymmetry in a Background Magnetic Field
• Meromorphic Scaling Flow of N=2 Supersymmetric SU(2) Yang-Mills with Matter
• RG Flow Irreversibility, C-Theorem and Topological Nature of 4D N=2 SYM
• Quantum Mechanics from General Relativity and the Quantum Friedmann Equation
• Deriving exact prepotential for $N=2$ supersymmetric Yang-Mills theories from superconformal anomaly with rank two gauge groups
• The structure of the exact effective action and the quark confinement in MSSM QCD
• Low Energy Effective Action in N=2 Yang-Mills as an Integrated Anomaly