Properties of the partition function of $\mathcal{N}=2$ supersymmetric QCD with massive matter

We study the different quantum phases that occur in massive $\mathcal{N}=2$ supersymmetric QCD with gauge groups $SU(2)$ and $SU(3)$ as the coupling $\mathrm{\Lambda }\mathrm{/}M$ is gradually increased from 0 to infinity. The phases can be identified by computing the exact partition function by saddle-points, combining supersymmetric localization and the Seiberg-Witten formalism. In all cases, we find two phases, a weak coupling and a strong coupling phase, separated by a critical point described by a superconformal field theory or involving superconformal sectors. In crossing the critical point, the dominant saddle-point hops from one singularity of the curve to another one. The theories seem to undergo a second-order phase transition with divergent susceptibility.