Prepotentials in N=2 SU(2) Supersymmetric Yang-Mills Theory with Massless Hypermultiplets

TL;DR

This paper computes the prepotential of N=2 SU(2) supersymmetric Yang-Mills theory with massless hypermultiplets, explicitly evaluating instanton corrections using elliptic curve techniques across different coupling regimes.

Contribution

It provides a detailed calculation of instanton effects in N=2 SU(2) theories with various flavors using Picard-Fuchs equations, clarifying flavor dependence in the low-energy effective action.

Findings

Explicit instanton correction evaluations for N_f=1,2,3.

Determination of flavor dependence in weak and strong coupling regimes.

Use of elliptic curves and Picard-Fuchs equations for precise calculations.

Abstract

We calculate the prepotential of the low-energy effective action for $N=2$ $SU(2)$ supersymmetric Yang-Mills theory with $N_f$ massless hypermultiplets ($N_f=1,\, 2,\, 3$). The precise evaluation of the instanton corrections is performed by making use of the Picard-Fuchs equations associated with elliptic curves. The flavor dependence of the instanton effect is determined explicitly both in the weak- and strong-coupling regimes.