Description
We calculate, via SUSY localization, the correlators of the operators whose vevs parametrize the Coulomb branches. In $4d$, we review the computation of the correlators of Wilson-'t Hooft line operators in $N=2$ gauge theories on $S^1 \times \mathbb{R}^3$. The results involve $Z_{\text{mono}}$, the monopole analog of the Nekrasov instanton partition function. For a class $\mathcal{S}$ theory, the correlators describe deformation quantization of the Hitchin moduli space in terms of Fenchel-Nielsen coordinates. In $3d$, we compute correlators of dressed monopole operators in $N=4$ gauge theories on $\mathbb{R}^3$ with omega deformation and develop similar stories. We compare our results with those obtained in other approaches. Based on arXiv:1111.4221 with Ito and Taki, as well as on a work in progress with Y. Yoshida.
