Abstract
We show that the supersymmetric partition function of three-dimensional \( \mathcal{N} \) =2 R-symmetric Chern-Simons-matter theories on the squashed S 3 and on S 2 × S 1 can be computed with the so-called Higgs branch localization method, alternative to the more standard Coulomb branch localization. For theories that could be completely Higgsed by Fayet-Iliopoulos terms, the path integral is dominated by BPS vortex strings sitting at two circles in the geometry. In this way, the partition function directly takes the form of a sum, over a finite number of points on the classical Coulomb branch, of a vortex-string times an antivortex-string partition functions.
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Benini, F., Peelaers, W. Higgs branch localization in three dimensions. J. High Energ. Phys. 2014, 30 (2014). https://doi.org/10.1007/JHEP05(2014)030
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DOI: https://doi.org/10.1007/JHEP05(2014)030