Partition function of N=2 supersymmetric gauge theory and two-dimensional Yang-Mills theory

We study four-dimensional $\mathcal{N}=2$ supersymmetric $U(N)$ gauge theory with $2N$ fundamental hypermultiplets in the self-dual $\mathrm{\ensuremath{\Omega}}$-background. The partition function simplifies at special points of the parameter space and is related to the partition function of two-dimensional Yang-Mills theory on ${S}^{2}$. We also consider the insertion of a Wilson loop operator in two-dimensional Yang-Mills theory and find the corresponding operator in the four-dimensional $\mathcal{N}=2$ gauge theory.