Matrix model approach to the N=2 U(N) gauge theory with matter in the fundamental representation

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We use matrix model technology to study the N=2 U(N) gauge theory with Nf massive hypermultiplets in the fundamental representation. We perform a completely perturbative calculation of the periods aᵢ and the prepotential F(a) up to the first instanton level, finding agreement with previous results in the literature. We also derive the Seiberg-Witten curve and differential from the large-M solution of the matrix model. We show that the two cases Nf<N and N ≤ Nf < 2N can be treated simultaneously.