# Quantum Geometry and Quiver Gauge Theories

Quantum Geometry and Quiver Gauge Theories 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 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications in Mathematical Physics Springer Journals

# Quantum Geometry and Quiver Gauge Theories

, Volume 357 (2) – Jan 11, 2018
49 pages

/lp/springer_journal/quantum-geometry-and-quiver-gauge-theories-NoS7ZKIW1M
Publisher
Springer Journals
Subject
Physics; Theoretical, Mathematical and Computational Physics; Mathematical Physics; Quantum Physics; Complex Systems; Classical and Quantum Gravitation, Relativity Theory
ISSN
0010-3616
eISSN
1432-0916
D.O.I.
10.1007/s00220-017-3071-y
Publisher site
See Article on Publisher Site

### Abstract

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 .

### Journal

Communications in Mathematical PhysicsSpringer Journals

Published: Jan 11, 2018

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