2014/04/30 by Jan Manschot, Boris Pioline, Ashoke Sen
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Computer science #Coulomb #Genus #Geometry #Higgs boson #Mathematical physics #Mathematical proof #Mathematics #Moduli space #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum mechanics #Quiver #Space (punctuation) #Superpotential #Supersymmetry #Theoretical physics #hep-th
paper · pdf · doi:10.5802/cml.41
published as Confluentes Mathematici 9 (2017) 2, 49-69 · 24 pages. v2: final version; minor changes, including a new diagram
arxiv created 2017/12/08 · openalex publication_date 2017/12/13 · arxiv updated 2018/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>χ</mml:mi> <mml:mi>y</mml:mi> </mml:msub> </mml:math> -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.