Partition function of $\mathcal{N}=2$ 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 $\Omega$-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. 
Xinyu Zhang
hep-th