Geodesic
The Coulomb Branch Formula for Quiver Moduli Spaces
Manschot, Jan1 ; Pioline, Boris2, 3 ; Sen, Ashoke4
1Univ 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
2CERN PH-TH, Case C01600, CERN, CH-1211 Geneva 23, Switzerland
3Sorbonne Universités; CNRS; UPMC Univ. Paris 06, UMR 7589, LPTHE, F-75005, Paris, France
4Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211019, India
Confluentes Mathematici, Tome 9 (2017) no. 2, pp. 49-69
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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.

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DOI : 10.5802/cml.41
Classification : 16G20, 37P45, 81T60, 83E50
Keywords: representations of quivers, moduli spaces, quiver quantum mechanics, bound states

Manschot, Jan  1   ; Pioline, Boris  2 , 3   ; Sen, Ashoke  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
Licence : CC-BY-NC-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Manschot, Jan; Pioline, Boris; Sen, Ashoke. The Coulomb Branch Formula for Quiver Moduli Spaces. Confluentes Mathematici, Tome 9 (2017) no. 2, pp. 49-69. doi: 10.5802/cml.41

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