Higgs branch localization in three dimensions

We show that the supersymmetric partition function of three-dimensional =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.