Abstract
We derive the exact vortex partition function in 2d \( \mathcal{N}=\left(2,2\right) \) gauge theory on the Ω-background, applying the localization scheme in the Higgs phase. We show that the partition function at a finite Ω-deformation parameter ϵ 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 Ω-deformation parameters (ϵ 1, ϵ 2).
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ArXiv ePrint: 1509.08630
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Fujimori, T., Kimura, T., Nitta, M. et al. 2d partition function in Ω-background and vortex/instanton correspondence. J. High Energ. Phys. 2015, 1–41 (2015). https://doi.org/10.1007/JHEP12(2015)110
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DOI: https://doi.org/10.1007/JHEP12(2015)110