Abstract
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 \({\Gamma}\).
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Communicated by X. Yin
Nikita Nekrasov is on leave of absence from Institut des Hautes Etudes Scientifiques, France, Institute of Theoretical and Experimental Physics, Russia and Institute for Information Transmission Problems, Lab. 5, Russia.
Vasily Pestun is on leave of absence from Institute of Theoretical and Experimental Physics, Russia.
Samson Shatashvili is on leave of absence from Euler International Mathematical Institute, St. Petersburg, Russia and Institute for Information Transmission Problems, Lab. 5, Russia.
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Nekrasov, N., Pestun, V. & Shatashvili, S. Quantum Geometry and Quiver Gauge Theories. Commun. Math. Phys. 357, 519–567 (2018). https://doi.org/10.1007/s00220-017-3071-y
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DOI: https://doi.org/10.1007/s00220-017-3071-y