On the Picard-Fuchs equations of the SW models

Abstract

We obtain the closed form of the Picard-Fuchs equations for $N=2$ supersymmetric Yang-Mills theories with classical Lie gauge groups. For a gauge group of rank $r$, there are $r-1$ regular and an exceptional differential equations. We describe the series solutions of the Picard-Fuchs equations in the semi-classical regime.

LaTex file, 6 pages, some references are added

References in corpus (8)

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• Picard-Fuchs Equations and Whitham Hierarchy in N=2 Supersymmetric SU(r+1) Yang-Mills Theory
• Simple Derivation of the Picard-Fuchs equations for the Seiberg-Witten Models
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• Instanton Correction of Prepotential in Ruijsenaars Model Associated with N=2 SU(2) Seiberg-Witten Theory
• Periods and Prepotential of N=2 Supersymmetric E_6 Yang-Mills Theory
• Evaluation of Periods via Fibrations in Seiberg-Witten Theories and in Type-II String
• 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