The Coulomb branch formula for quiver moduli spaces

Abstract

In recent series of works, by translating properties of multi-cent ered supersymmetric black holes into the language of quiver representations, we proposed a f ormula that expresses the Hodge numbers of the moduli space of semi-stable representation s 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 b ranch formula, spelling out mathematical details but leaving out proofs and physical motiva tions.