A New Derivation of the Picard-Fuchs Equations for Effective $N=2$ Super Yang-Mills Theories

Abstract

A new method to obtain the Picard-Fuchs equations of effective $N=2$ supersymmetric gauge theories in 4 dimensions is developed. It includes both pure super Yang-Mills and supersymmetric gauge theories with massless matter hypermultiplets. It applies to all classical gauge groups, and directly produces a decoupled set of second-order, partial differential equations satisfied by the period integrals of the Seiberg-Witten differential along the 1-cycles of the algebraic curves describing the vacuum structure of the corresponding $N=2$ theory.

Latex version, 43 pages, a few cosmetic changes and some references added

References in corpus (29)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• New Phenomena in SU(3) Supersymmetric Gauge Theory
• Simple Singularities and N=2 Supersymmetric Yang-Mills Theory
• The Vacuum Structure and Spectrum of N=2 Supersymmetric SU(N) Gauge Theory
• Instantons and recursion relations in N=2 Susy gauge theory
• The Moduli Space of N=2 SUSY QCD and Duality in N=1 SUSY QCD
• The Coulomb Phase of N=2 Supersymmetric QCD
• Dynamics of $SU(N)$ Supersymmetric Gauge Theory
• On the Quantum Moduli Space of Vacua of $N=2$ Supersymmetric $SU(N_c)$ Gauge Theories
• Topological Reduction of 4D SYM to 2D $\sigma$--Models
• Nonperturbative Effective Actions of N=2 Supersymmetric Gauge Theories
• The Vacuum Structure of N=2 SuperQCD with Classical Gauge Groups
• Study of $N=2$ Superconformal Field Theories in $4$ Dimensions
• On the Monodromies of N=2 Supersymmetric Yang-Mills Theory with Gauge Group SO(2n)
• On the Quantum Moduli Space of N=2 Supersymmetric Gauge Theories
• The Moduli Space and Monodromies of N=2 Supersymmetric \(SO(2r+1) \) Yang-Mills Theory
• Curves of Marginal Stability and Weak and Strong-Coupling BPS Spectra in $N=2$ Supersymmetric QCD
• Nonperturbative Renormalization Group Equation and Beta Function in N=2 SUSY Yang-Mills
• Hyperelliptic curves for Supersymmetric Yang-Mills
• Prepotentials in N=2 SU(2) Supersymmetric Yang-Mills Theory with Massless Hypermultiplets
• Exact and microscopic one-instanton calculations in N=2 supersymmetric Yang-Mills theories
• The Moduli Space and Monodromies of the $N=2$ Supersymmetric Yang-Mills Theory with any Lie Gauge Groups
• Exceptional Equivalences in N=2 Supersymmetric Yang-Mills Theory
• Prepotential of N=2 SU(2) Yang-Mills gauge theory coupled with a massive matter multiplet
• Numerical evidence for the spin-Peierls state in the frustrated quantum antiferromagnet
• Simple Calculation of Instanton Corrections in Massive N=2 SU(3) SYM
• The Picard-Fuchs Equations, Monodromies and Instantons in the N=2 Susy Gauge Theories
• Exact Multiplets of Spontaneously Broken Discrete Global Symmetries: the Example of $N=2$ Susy QCD

Cited by in corpus (22)

• Introduction to Seiberg-Witten Theory and its Stringy Origin
• Softly Broken N=2 QCD with Massive Quark Hypermultiplets, I
• Non-holomorphic terms in N=2 SUSY Wilsonian actions and RG equation
• Seiberg--Witten Duality in Dijkgraaf--Vafa Theory
• One-Instanton Test of a Seiberg-Witten Curve from M-theory: the Antisymmetric Representation of SU(N)
• Flat Coordinates, Topological Landau-Ginzburg Models and the Seiberg-Witten Period Integrals
• Picard-Fuchs Equation and Prepotential of Five Dimensional SUSY Gauge Theory Compactified on a Circle
• Simple Calculation of Instanton Corrections in Massive N=2 SU(3) SYM
• Two antisymmetric hypermultiplets in N=2 SU(N) gauge theory: Seiberg-Witten curve and M-theory interpretation
• On the WDVV Equation and M-Theory
• Picard-Fuchs Equations and Whitham Hierarchy in N=2 Supersymmetric SU(r+1) Yang-Mills Theory
• The Picard-Fuchs equation in classical and quantum physics: Application to higher-order WKB method
• Moduli Space Metric of N=2 Supersymmetric SU(N) Gauge Theory and the Enhancon
• Vacuum structure of spontaneously broken N=2 supersymmetric gauge theory
• Exploring the Strong-Coupling Region of $SU(N)$ Seiberg-Witten Theory
• Picard-Fuchs Ordinary Differential Systems in N=2 Supersymmetric Yang-Mills Theories
• RG Flow Irreversibility, C-Theorem and Topological Nature of 4D N=2 SYM
• Instanton Correction of Prepotential in Ruijsenaars Model Associated with N=2 SU(2) Seiberg-Witten Theory
• Geometric Engineering of Seiberg-Witten Theories with Massive Hypermultiplets
• One-Instanton Prepotentials from WDVV equations in N=2 Supersymmetric SU(4) Yang-Mills Theory
• Direct Derivation of Scaling Relation of Prepotential in N=2 Supersymmetric G_2 Yang-Mills Theory
• An Algebraic Geometry Method for Calculating DOS for 2D tight binding models