Abstract
Abstract In previous work we have shown that the equivariant index of multi-centered $ \mathcal{N}=2 $ black holes localizes on collinear configurations along a fixed axis. Here we provide a general algorithm for enumerating such collinear configurations and computing their contribution to the index. We apply this machinery to the case of black holes described by quiver quantum mechanics, and give a systematic prescription — the Coulomb branch formula — for computing the cohomology of the moduli space of quiver representations. For quivers without oriented loops, the Coulomb branch formula is shown to agree with the Higgs branch formula based on Reineke’s result for stack invariants, even when the dimension vector is not primitive. For quivers with oriented loops, the Coulomb branch formula parametrizes the Poincaré polynomial of the quiver moduli space in terms of single-centered (or pure-Higgs) BPS invariants, which are conjecturally independent of the stability condition (i.e. the choice of Fayet-Iliopoulos parameters) and angular-momentum free. To facilitate further investigation we provide a Mathematica package “CoulombHiggs.m” implementing the Coulomb and Higgs branch formulae.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
