Localization of three-dimensional $\mathcal{N}=2$ supersymmetric theories on $S^1 \times D^2$

DOI10.1093/PTEP/PTAA136zbMATH Open1477.81094arXiv1409.6713OpenAlexW2739595407MaRDI QIDQ5157629

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Publication date: 19 October 2021

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Abstract: We study three dimensional $mathcalN=2$ supersymmetric Chern-Simons-Matter theories on the direct product of a circle and a two dimensional hemisphere ($S^{1}imes{D}^2$) with specified boundary conditions by the method of localization. We construct boundary interactions to cancel the supersymmetric variation of the three dimensional superpotential term and the Chern-Simons term and show inflows of the bulk-boundary anomalies. It finds that the boundary conditions induce two dimensional $mathcalN=(0,2)$ type supersymmetry on the boundary torus. We also study the relation between the 3d-2d coupled partition function of our model and three dimensional holomorphic blocks.

Full work available at URL: https://arxiv.org/abs/1409.6713

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