Quantum Geometry and Quiver Gauge Theories

By N. Nekrasov, Vasily Pestun, S. Shatashvili. 2013

207 citations recorded by the source corpus.

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 $${\mathbb{T}^{d} \times \mathbb{R}^{2}_{\epsilon}}$$Td×Rϵ2 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 $${\mathbf{Y}_{\epsilon}(\mathfrak{g}_{\Gamma})}$$Yϵ(gΓ), quantum affine algebra $${\mathbf{U}^{\mathrm{aff}}_q(\mathfrak{g}_{\Gamma})}$$Uqaff(gΓ), or the quantum elliptic algebra $${\mathbf{U}^{\mathrm{ell}}_{q,p}(\mathfrak{g}_{\Gamma})}$$Uq,pell(gΓ) associated to Kac–Moody algebra $${\mathfrak{g}_{\Gamma}}$$gΓ for quiver $${\Gamma}$$Γ.

Subfields: Atomic and Molecular Physics, and Optics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/58d4d49c28dc2f406e37211f96211778292f5e32

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Citations in the corpus

Defects and quantum Seiberg-Witten geometry (2014, methodology): “that we have focussed on in this paper. Recently, in [75] this correspondence was extended and systematized to a large class four dimensional quiver gauge theories of nite and ane ADE type. Later in [44] the ve and six-dimensional versions of the Seiberg-Witten geometry together with its quantum def”
Quiver W-algebras (2015, methodology): “Examples We consider a few examples to illustrate the equivalence between gauge-theory formalism [2, 3, 7] and the operator formalism [1, 5, 9, 15].”
Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2 (2015, background): “See also [65,66] for a study of the Nekrasov partition function for this class of theories.”
BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters (2015, methodology): “This function plays an important role in quantization of the symplectic manifold P and the Bethe/gauge correspondence [89, 96, 90, 87, 86].”
Topological Strings from Quantum Mechanics (2014, background): “Inspired by the work of [13], it was found in [16, 17, 18] that the perturbative WKB quantization condition for the spectrum of these operators is closely related to the NS limit of the refined topological string on X.”