The paper constructs dictionaries equating the vacuum equations of 4D N=1 BCD-type gauge theories on D^2×T^2 with the Bethe ansatz equations of open XYZ spin chains by fixing mass and boundary parameters to force the match.
2d Partition Function in Omega-background and Vortex/Instanton Correspondence
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abstract
We derive the exact vortex partition function in 2d $\mathcal{N}$ = (2,2) gauge theory on the Omega-background, applying the localization scheme in the Higgs phase. We show that the partition function at a finite Omega-deformation parameter $\epsilon$ satisfies a system of differential equations, which can be interpreted as a quantized version of the twisted F-term equations characterizing the SUSY vacua. Using the differential equations derived in this paper, we show the correspondence between the partition function of the two-dimensional vortex string worldsheet theory and the Nekrasov partition function at the root of Higgs branch of the four-dimensional $\mathcal{N}$ = 2 theory with two Omega-deformation parameters $(\epsilon_1,\epsilon_2)$.
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Spin Chain Integrability as a Supersymmetric Gauge Duality
The paper constructs dictionaries equating the vacuum equations of 4D N=1 BCD-type gauge theories on D^2×T^2 with the Bethe ansatz equations of open XYZ spin chains by fixing mass and boundary parameters to force the match.