On Higgs Branch Localization of Seiberg-Witten Theories on Ellipsoid

Abstract

In this note, we consider so-called "Higgs Branch Localization" for four dimensional N=2 field theories on 4d ellipsoid. We find a new set of saddle point equations arising from additional Higgs branch deformation term, whose solutions include both Higgs branch and BPS instanton-vortex mixed configurations. By evaluating the contour integral, we also demonstrate the ellipsoid partition almost factorizes into purely b and 1/b dependent parts, using SQCD as an explicit example. We identify various factorized parts with the ellipsoid partition function of two dimensional N=(2,2) SQCDA, which is precisely the vortex world volume theory. We also give physical interpretation for the non-factorizable parts and discuss future directions.

arXiv comment30 pages, 2 Figures. Instanton calculation corrected and various other clarifications and comments added, reference list Improved

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• Intersecting Surface Defects and Two-Dimensional CFT
• Supersymmetric localization in two dimensions
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• 3d Expansions of 5d Instanton Partition Functions
• Orbifolds, Defects and Sphere Partition Function
• Bootstrapping the $S^5$ partition function
• Partition Functions of $\mathcal{N}=1$ Gauge Theories on $S^2\times {\mathbb{R}}_{\epsilon }^2$ and Duality
• Intersecting Surface defects and 3d Superconformal indices
• Vortex-strings in N=2 quiver X U(1) theories