| Article | |
| Report number | arXiv:1302.5498 ; BONN-TH-2013-03 ; CERN-PH-TH-2013-030 ; HRI-ST-1302 ; BONN-TH-2013-03 ; CERN-PH-TH-2013-030 ; HRI-ST-1302 |
| Title | On the Coulomb and Higgs branch formulae for multi-centered black holes and quiver invariants |
| Author(s) | Manschot, Jan (Bonn U. ; Bonn, Max Planck Inst., Math.) ; Pioline, Boris (CERN ; Paris, LPTHE) ; Sen, Ashoke (Harish-Chandra Res. Inst.) |
| Publication | 2013 |
| Imprint | 25 Feb 2013 |
| Number of pages | 46 |
| Note | Comments: 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 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 |
| In: | JHEP 05 (2013) 166 |
| DOI | 10.1007/JHEP05(2013)166 |
| Subject category | Particle Physics - Theory |
| Abstract | 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 Poincar\'e 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. |
| Copyright/License | Preprint: © 2013-2024 CERN (License: CC-BY-3.0) |
Corresponding record in: Inspire
Record created 2013-02-25, last modified 2023-10-04