Quantum Geometry and Quiver Gauge Theories

Nikita Nekrasov; Vasily Pestun; Samson Shatashvili

doi:10.1007/s00220-017-3071-y

Quantum Geometry and Quiver Gauge Theories

Nikita Nekrasov
, Vasily Pestun
, Samson Shatashvili

Simons Center for Geometry & Physics

Stony Brook University

Research output: Contribution to journal › Article › peer-review

86 Scopus citations

Abstract

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×Rϵ2 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 and the Yangian Y_ϵ(g_Γ) , quantum affine algebra Uqaff(gΓ), or the quantum elliptic algebra Uq,pell(gΓ) associated to Kac–Moody algebra g_Γ for quiver Γ.

Original language	English
Pages (from-to)	519-567
Number of pages	49
Journal	Communications in Mathematical Physics
Volume	357
Issue number	2
DOIs	https://doi.org/10.1007/s00220-017-3071-y
State	Published - Jan 1 2018

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abstract = "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×Rϵ2 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 and the Yangian Yϵ(gΓ) , quantum affine algebra Uqaff(gΓ), or the quantum elliptic algebra Uq,pell(gΓ) associated to Kac–Moody algebra gΓ for quiver Γ.",

author = "Nikita Nekrasov and Vasily Pestun and Samson Shatashvili",

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AU - Nekrasov, Nikita

AU - Pestun, Vasily

AU - Shatashvili, Samson

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N2 - 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×Rϵ2 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 and the Yangian Yϵ(gΓ) , quantum affine algebra Uqaff(gΓ), or the quantum elliptic algebra Uq,pell(gΓ) associated to Kac–Moody algebra gΓ for quiver Γ.

AB - 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×Rϵ2 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 and the Yangian Yϵ(gΓ) , quantum affine algebra Uqaff(gΓ), or the quantum elliptic algebra Uq,pell(gΓ) associated to Kac–Moody algebra gΓ for quiver Γ.

UR - https://www.scopus.com/pages/publications/85040362539

U2 - 10.1007/s00220-017-3071-y

DO - 10.1007/s00220-017-3071-y

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JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

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ER -

Quantum Geometry and Quiver Gauge Theories

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