On Higgs Branch Localization of Seiberg-Witten Theories on Ellipsoid

Understand

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.