2013/02/28 by Jan Manschot, Boris Pioline, Ashoke Sen · 56 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Coulomb #Higgs boson #Mathematics #Moduli space #Nonlinear Waves and Solitons #Particle physics #Physics #Pure mathematics #Quantum mechanics #Quiver #hep-th #math.AG #math.RT
paper · pdf · doi:10.1007/jhep05(2013)166
published in Journal of High Energy Physics 2013(5) (Springer Nature) · 45 pages, 1 figure; v2 (after publication in JHEP): New recursion scheme introduced in Note Added, 4.31-4.34; Appendix updated to document new features of the Mathematica package "CoulombHiggs.m" v2.0, available along with example files from the submission source, or from http://www.lpthe.jussieu.fr/~pioline/computing.html
openalex publication_date 2013/05/01 · arxiv created 2013/09/30 · arxiv updated 2015/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A bstract In previous work we have shown that the equivariant index of multi-centered 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 M athematica package “CoulombHiggs.m” implementing the Coulomb and Higgs branch formulae.