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

TL;DR

This paper employs matrix model techniques to analyze N=2 U(N) gauge theories with fundamental matter, deriving the Seiberg-Witten curve and prepotential perturbatively up to the first instanton, confirming previous results.

Contribution

It introduces a matrix model approach to compute the prepotential and Seiberg-Witten curve for N=2 U(N) gauge theories with fundamental matter, including cases with N_f less than or equal to N.

Findings

Perturbative calculation of periods and prepotential matches known results.

Derived the Seiberg-Witten curve from the matrix model solution.

Unified treatment of different N_f regimes within the matrix model framework.

Abstract

We use matrix model technology to study the N=2 U(N) gauge theory with N_f massive hypermultiplets in the fundamental representation. We perform a completely perturbative calculation of the periods a_i 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 N_f<N and N \le N_f < 2N can be treated simultaneously.