Higgs branch localization of 3d N=2 theories

TL;DR

<3-5 sentence high-level summary> The paper develops Higgs branch localization for 3d $\mathcal{N}=2$ gauge theories on the ellipsoid $S_b^3$ and on $S^1\times S^2$, demonstrating that partition functions factorize into products of vortex and anti-vortex partition functions, i.e. holomorphic blocks. By introducing a dedicated deformation term $\mathcal{L}_H$ the authors reveal Higgs-sector saddles at the north and south poles, yielding explicit vortex data that reproduces the factorization observed in Coulomb-branch results and in superconformal indices. The analysis extends beyond simple cases to $U(N)$ theories with arbitrary fundamental/anti-fundamental matter and mass-deformed $\mathcal{N}=4$ theories (the $\mathcal{N}=2^*$ limit), and it clarifies the role of vortex worldline theories in building the full partition function. Additionally, the work discusses Wilson loops and outlines potential applications to other BPS observables and string/M-theory dualities through holomorphic blocks.

Abstract

We study N=2 supersymmetric gauge theories on squashed 3-sphere and S^1xS^2. Recent studies have shown that the partition functions in a class of N=2 theories have factorized forms in terms of vortex and anti-vortex partition functions by explicitly evaluating matrix integrals obtained from Coulomb branch localization. We directly derive this structure by performing Higgs branch localization. It turns out that more general N=2 theories have this factorization property. We also discuss the factorization of supersymmetric Wilson loop.