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

TL;DR

This paper introduces a novel method to derive Picard-Fuchs equations for effective N=2 supersymmetric gauge theories, applicable to various gauge groups and matter content, enhancing understanding of their vacuum structure.

Contribution

It presents a new approach to obtain Picard-Fuchs equations directly from algebraic curves in N=2 gauge theories, covering pure and matter-coupled cases for all classical gauge groups.

Findings

Derivation of second-order PDEs for period integrals

Applicable to all classical gauge groups

Includes theories with massless matter hypermultiplets

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.