Exact Results in Quiver Quantum Mechanics and BPS Bound State Counting

TL;DR

This paper computes the exact partition function of N=4 supersymmetric quiver quantum mechanics using localization, confirming mathematical predictions and exploring Wilson loop expectation values.

Contribution

It provides an exact evaluation of the partition function in the Higgs phase, matching mathematical formulas and including non-coprime cases.

Findings

Partition function matches Poincare polynomials and wall crossing formulas.

Localization reduces path integral to fixed points solving BRST, D-term, and F-term equations.

Wilson loop expectation values are computed exactly.

Abstract

We exactly evaluate the partition function (index) of N=4 supersymmetric quiver quantum mechanics in the Higgs phase by using the localization techniques. We show that the path integral is localized at the fixed points, which are obtained by solving the BRST equations, and D-term and F-term conditions. We turn on background gauge fields of R-symmetries for the chiral multiplets corresponding to the arrows between quiver nodes, but the partition function does not depend on these R-charges. We give explicit examples of the quiver theory including a non-coprime dimension vector. The partition functions completely agree with the mathematical formulae of the Poincare polynomials (chi_y-genus) and the wall crossing for the quiver moduli spaces . We also discuss exact computation of the expectation values of supersymmetric (Q-closed) Wilson loops in the quiver theory.