The Coulomb Branch Formula for Quiver Moduli Spaces

Abstract

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 ${\chi }_y$-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.

24 pages. v2: final version; minor changes, including a new diagram

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Cited by in corpus (13)

• Witten Index and Wall Crossing
• Vafa-Witten invariants from exceptional collections
• Attractor flow trees, BPS indices and quivers
• 5D BPS Quivers and KK Towers
• Black holes and higher depth mock modular forms
• Regge Trajectories in $\mathcal{N}=2$ Supersymmetric Yang-Mills Theory
• Multi-centered black holes, scaling solutions and pure-Higgs indices from localization
• Discrete Integrable Systems, Supersymmetric Quantum Mechanics, and Framed BPS States - I
• BPS Dendroscopy on Local $P^2$
• About the Absence of Exotics and the Coulomb Branch Formula
• Attractor invariants, brane tilings and crystals
• A twist on multicenter AdS${}_2$ solutions
• Mutation, Witten Index, and Quiver Invariant