Exact results in four-dimensional Gauge Theories from Matrix models

Abstract

We use localization and the Seiberg-Witten curve to exactly compute supersymmetric observables in different ${\cal N}=2$ four-dimensional theories. We first consider ${\cal N}=2$ SQCD with gauge group $SU(2)$ and two massive flavors. We compute the exact free energy, including all instanton contributions, and show that the theory undergoes a second-order quantum phase transition at a critical coupling. In the second part, we use localization to compute large $N$ correlation functions in superconformal field theories.