Cellular algebra

Supersymmetry

Physics

Algebra over a field

Algebra representation

Archaeology

Quiver

Superpotential

Gauge theory

Quantum affine algebra

Pure mathematics

Geometry

Yangian

Omega

Mathematics

Mathematical physics

Gauge (firearms)

Quantum mechanics

Quantum

History

Torus

Communications in Mathematical Physics

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 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 $${\Gamma}$$ .

Quantum Geometry and Quiver Gauge Theories