The Picard-Fuchs Equations, Monodromies and Instantons in the N=2 Susy Gauge Theories

TL;DR

This paper derives Picard-Fuchs equations for N=2 supersymmetric SU(2) gauge theories with various matter content, analyzes monodromies, and computes instanton expansions to deepen understanding of their quantum moduli spaces.

Contribution

It constructs explicit Picard-Fuchs equations for N=2 SU(2) theories with different flavors and computes monodromies and instanton expansions, providing new exact results.

Findings

Monodromy matrices for N_f=0 theory determined from Picard-Fuchs solutions.

Exact monodromies computed using Seiberg-Witten solutions.

Instanton expansions of periods presented for N_f=0 and N_f=3 theories.

Abstract

We construct the Picard-Fuchs equations of the $N=2$ supersymmetric $SU(2)$ gauge theories with $N_f=0,1,3$ matter multiplets. For the $N_f=0$ theory from the solutions of the Picard-Fuchs equation the monodromy matrices on the quantum moduli space are determined. We analyze the Seiberg-Witten solutions to compute monodromies exactly and present the instanton expansion of the periods for the $N_f=0,3$ theories.