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