The Coulomb Branch Formula for Quiver Moduli Spaces
Confluentes Mathematici, Volume 9 (2017) no. 2, pp. 49-69.

In recent series of works, by translating properties of multi-centered supersymmetric black holes into the language of quiver representations, we proposed a formula that expresses the Hodge numbers of the moduli space of semi-stable representations of quivers with generic superpotential in terms of a set of invariants associated to ‘single-centered’ or ‘pure-Higgs’ states. The distinguishing feature of these invariants is that they are independent of the choice of stability condition. Furthermore they are uniquely determined by the χ y -genus of the moduli space. Here, we provide a self-contained summary of the Coulomb branch formula, spelling out mathematical details but leaving out proofs and physical motivations.

Published online:
DOI: 10.5802/cml.41
Classification: 16G20, 37P45, 81T60, 83E50
Keywords: representations of quivers, moduli spaces, quiver quantum mechanics, bound states
Jan Manschot 1; Boris Pioline 2, 3; Ashoke Sen 4

1 Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR5208, Institut Camille Jordan, F-69622 Villeurbanne Cedex, France Current address: School of Mathematics, Trinity College, College Green, Dublin 2, Ireland
2 CERN PH-TH, Case C01600, CERN, CH-1211 Geneva 23, Switzerland
3 Sorbonne Universités; CNRS; UPMC Univ. Paris 06, UMR 7589, LPTHE, F-75005, Paris, France
4 Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211019, India
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
     author = {Jan Manschot and Boris Pioline and Ashoke Sen},
     title = {The {Coulomb} {Branch} {Formula} for {Quiver} {Moduli} {Spaces}},
     journal = {Confluentes Mathematici},
     pages = {49--69},
     publisher = {Institut Camille Jordan},
     volume = {9},
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     year = {2017},
     doi = {10.5802/cml.41},
     zbl = {1392.16015},
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     language = {en},
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Jan Manschot; Boris Pioline; Ashoke Sen. The Coulomb Branch Formula for Quiver Moduli Spaces. Confluentes Mathematici, Volume 9 (2017) no. 2, pp. 49-69. doi : 10.5802/cml.41.

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