The Coulomb Branch Formula for Quiver Moduli Spaces

TL;DR

This paper presents a formula that computes the Hodge numbers of quiver moduli spaces using invariants related to single-centered states, independent of stability conditions, linking to the moduli space's $hi_y$-genus.

Contribution

It introduces a Coulomb branch formula that expresses quiver moduli space invariants in terms of stability-independent single-centered invariants.

Findings

The formula relates Hodge numbers to single-centered invariants.

Invariants are uniquely determined by the $hi_y$-genus.

The approach is self-contained and mathematically detailed.

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.