We study macroscopically two dimensional $${\mathcal{N}=(2,2)}$$ N = ( 2 , 2 ) supersymmetric gauge theories constructed by compactifying the quiver gauge theories with eight supercharges on a product $${\mathbb{T}^{d} \times \mathbb{R}^{2}_{\epsilon}}$$ T d × R ϵ 2 of a d-dimensional torus and a two dimensional cigar with $${\Omega}$$ Ω -deformation. We compute the universal part of the effective twisted superpotential. In doing so we establish the correspondence between the gauge theories and the Yangian $${\mathbf{Y}_{\epsilon}(\mathfrak{g}_{\Gamma})}$$ Y ϵ ( g Γ ) , quantum affine algebra $${\mathbf{U}^{\mathrm{aff}}_q(\mathfrak{g}_{\Gamma})}$$ U q aff ( g Γ ) , or the quantum elliptic algebra $${\mathbf{U}^{\mathrm{ell}}_{q,p}(\mathfrak{g}_{\Gamma})}$$ U q , p ell ( g Γ ) associated to Kac–Moody algebra $${\mathfrak{g}_{\Gamma}}$$ g Γ for quiver $${\Gamma}$$ Γ .
Communications in Mathematical Physics – Springer Journals
Published: Jan 11, 2018
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