Exact Results in Quiver Quantum Mechanics and BPS Bound State Counting

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.

arXiv comment40 pages, 7 figures; v2: minor corrections and references are added; v3: references added, typos corrected, discrepancy in the non-coprime case resolved

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• Line defects as brane boxes in Gaiotto-Maldacena geometries
• Coulomb Branch Localization in Quiver Quantum Mechanics
• Regge Trajectories in $\mathcal{N}=2$ Supersymmetric Yang-Mills Theory
• Quiver indices and Abelianization from Jeffrey-Kirwan residues
• Multi-centered black holes, scaling solutions and pure-Higgs indices from localization
• The Volume of the Quiver Vortex Moduli Space
• Exact Results in Discretized Gauge Theories
• Kazakov-Migdal model on the Graph and Ihara Zeta Function
• SUSY in Silico: numerical D-brane bound state spectroscopy
• Pure-Higgs states from the Lefschetz-Sommese theorem
• Tunnels Under Geometries (or Instantons Know Their Algebras)
• Spectral Sequences and Vacua in N = 2 Gauged Linear Quantum Mechanics with Potentials
• Gauge origami and quiver W-algebras IV: Pandharipande--Thomas $qq$-characters