Ellipsoid partition function from Seiberg-Witten monopoles

TL;DR

This paper investigates the Higgs branch localization of N=2 supersymmetric theories on the four-sphere, revealing that the path integral is dominated by vortex-like configurations and singular Seiberg-Witten monopoles, leading to a new partition function formulation.

Contribution

It introduces a detailed analysis of localization equations on the four-sphere, incorporating vortex configurations and monopoles into the partition function calculation.

Findings

Partition function dominated by vortex-like configurations and monopoles.

Explicit form of the partition function including monopole contributions.

Enhanced understanding of Higgs branch localization on curved manifolds.

Abstract

We study Higgs branch localization of N=2 supersymmetric theories placed on compact Euclidean manifolds. We analyze the resulting localization equations in detail on the four-sphere and find that in this case the path integral is dominated by vortex-like configurations as well as singular Seiberg-Witten monopoles located at the north and south pole. The partition function is written accordingly.