Prepotentials in N=2 Supersymmetric SU(3) YM-Theory with Massless Hypermultiplets

We explicitly determine the instanton corrections to the prepotential for N=2 supersymmetric SU(3) Yang-Mills theory with massless hypermultiplets in the weak coupling regions \(u\to\infty\) and \(v\to\infty\). We construct the Picard-Fuchs equations for \(N_f<6\) and calculate the monodromies using Picard-Lefschetz theorem for \(N_f=2,4\). For all \(N_f<6\) the instanton corrections to the prepotential are determined using the relation between \(Tr <\phi^2>\) and the prepotential.