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We study three dimensional $\mathcal{N}=2$ supersymmetric Chern-Simons-Matter theories on the direct product of a circle and a two dimensional hemisphere ($S^1 \times D^2$) with specified boundary conditions by the method of localization.
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A. Gerasimov, D. Lebedev, S. Oblezin, “From Archimedean L-factors and Topological Field Theories,” Lett. Math. Phys. 96, 285-297 (2011)
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D. L. Jafferis, “The Exact Superconformal R-Symmetry Extremizes Z,” JHEP 1205
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2014
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C. Hwang, H. C. Kim and J. Park, “Factorization of the 3d superconformal index,” JHEP 1408
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M. Fujitsuka, M. Honda and Y. Yoshida, “Higgs branch localization of 3d N= 2 theories,” PTEP 2014
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F. Benini and W. Peelaers, “Higgs branch localization in three dimensions,” JHEP 1405
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2016
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