We study macroscopically two dimensional $\mathcal{ N}=(2,2)$ supersymmetric gauge theories constructed by compactifying the quiver gauge theories with eight supercharges on a product $\mathbb{ T}^{ d} \times \mathbb{ R}^{ 2}_{ \epsilon}$ of a $d$-dimensional torus and a two dimensional cigar with $\Omega$-deformation. We compute the universal part of the effective twisted superpotential. In doing so we establish the correspondence between the gauge theories, quantization of the moduli spaces of instantons on $\mathbb{ R}^{ 2-d} \times \mathbb{ T}^{ 2+d}$ and singular monopoles on $\mathbb{ R}^{ 2-d} \times \mathbb{ T}^{ 1+d}$, for $d=0,1,2$, and the Yangian $\mathbf{ Y}_{ \epsilon}(\mathfrak{ g}_{ \Gamma})$, quantum affine algebra $\mathbf{ U}^{ \mathrm{ aff}}_q(\mathfrak{ g}_{ \Gamma})$, or the quantum elliptic algebra $\mathbf{ U}^{ \mathrm{ ell}}_{ q,p}(\mathfrak{ g}_{ \Gamma})$ associated to Kac-Moody algebra $\mathfrak{ g}_{ \Gamma}$ for quiver $\Gamma$.
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