Quantum geometry and quiver gauge theories

الأصل · EN

We study macroscopically two dimensional N=(2,2) supersymmetric gauge theories constructed by compactifying the quiver gauge theories with eight supercharges on a product Tᵈ × R²ε of a d-dimensional torus and a two dimensional cigar with Ω-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 R²⁻ᵈ × T²⁺ᵈ and singular monopoles on R²⁻ᵈ × T¹⁺ᵈ, for d=0,1,2, and the Yangian Yε(gΓ), quantum affine algebra Uaffq(gΓ), or the quantum elliptic algebra Uellq,ₚ(gΓ) associated to Kac-Moody algebra gΓ for quiver Γ.