Coulomb Branch Localization in Quiver Quantum Mechanics

TL;DR

This paper develops a method to exactly compute refined indices in N=4 supersymmetric quiver quantum mechanics using Coulomb branch localization, providing a new perspective and confirming results from Higgs branch localization.

Contribution

It introduces Coulomb branch localization for calculating refined indices in supersymmetric quiver quantum mechanics, complementing Higgs branch methods.

Findings

Refined indices can be expressed as sums over Coulomb branch fixed points.

Coulomb and Higgs branch localization results agree.

Provides a space-time interpretation of Coulomb branch fixed points.

Abstract

We show how to exactly calculate the refined indices of N=4 U(1) times U(N) supersymmetric quiver quantum mechanics in the Coulomb branch by using the localization technique. The Coulomb branch localization is discussed from the viewpoint of both non-linear and gauged linear sigma models. A classification of fixed points in the Coulomb branch differs from one in the Higgs branch, but the derived indices completely agree with the results which were obtained by the localization in the Higgs branch. In the Coulomb branch localization, the refined indices can be written as a summation over different sets of the Coulomb branch fixed points. We also discuss a space-time picture of the fixed points in the Coulomb branch.