# Coulomb branch localization in quiver quantum mechanics

Ohta, Kazutoshi (Institute of Physics, Meiji Gakuin University, 1518 Kamikurata-cho, Yokohama, 244-8539, Japan) ; Sasai, Yuya (Institute of Physics, Meiji Gakuin University, 1518 Kamikurata-cho, Yokohama, 244-8539, Japan)

17 February 2016

Abstract: We show how to exactly calculate the refined indices of N = 4 U 1 × U N $\mathcal{N}=4\;\mathrm{U}(1)\times \mathrm{U}(N)$ 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.

Published in: JHEP 1602 (2016) 106