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Title of Journal: J High Energ Phys

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Abbravation: Journal of High Energy Physics

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Springer-Verlag

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10.1006/jmbi.1995.0546

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1029-8479

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On the Coulomb and Higgs branch formulae for multi

Authors: Jan Manschot Boris Pioline Ashoke Sen
Publish Date: 2013/05/31
Volume: 2013, Issue: 5, Pages: 166-
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Abstract

In previous work we have shown that the equivariant index of multicentered mathcalN=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 singlecentered or pureHiggs BPS invariants which are conjecturally independent of the stability condition ie the choice of FayetIliopoulos parameters and angularmomentum free To facilitate further investigation we provide a Mathematica package “CoulombHiggsm” implementing the Coulomb and Higgs branch formulaeThis article is published under an open access license Please check the Copyright Information section for details of this license and what reuse is permitted If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and reuse information please contact the Rights and Permissions team

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