Partition Functions of $\mathcal{N}=1$ Gauge Theories on $S^2\times {\mathbb{R}}_{\epsilon }^2$ and Duality

Taro Kimura, Jun Nian, Peng Zhao

We compute the partition functions of $\mathcal{N}=1$ gauge theories on $S^2\times {\mathbb{R}}_{\epsilon }^2$ using supersymmetric localization. The path integral reduces to a su…