2d partition function in \(\Omega\)-background and vortex/instanton correspondence

DOI10.1007/JHEP12(2015)110zbMATH Open1388.81812arXiv1509.08630MaRDI QIDQ2636303

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Publication date: 31 May 2018

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Abstract: We derive the exact vortex partition function in 2d $mathcalN$ = (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 $mathcalN$ = 2 theory with two Omega-deformation parameters $(epsilo{n}_1,epsilo{n}_2)$.

Full work available at URL: https://arxiv.org/abs/1509.08630

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