From Black Holes to Quivers

TL;DR

This work develops a cohesive framework linking the Higgs-branch cohomology of quiver quantum mechanics to the microstate structure of multi-centered black holes. By positing a moduli-independent, pure-Higgs single-centered input and a generalized Coulomb-branch formula, the authors reconstruct the full moduli-space cohomology (Poincaré and Dolbeault data) from BPS invariants, successfully testing on Abelian and non-Abelian quivers with one or more loops. They integrate Lefschetz hyperplane methods, Riemann–Roch, and Harder–Narasimhan recursion to compute cohomology directly and to fix the unknown pure-Higgs contributions, achieving agreement across Higgs- and Coulomb-branch descriptions. The results illuminate the role of middle cohomology states as intrinsic Higgs (pure-Higgs) micro-states and provide practical counting techniques for these states, with implications for black hole microstate counting and the structure of BPS spectra in string compactifications.

Abstract

Middle cohomology states on the Higgs branch of supersymmetric quiver quantum mechanics - also known as pure Higgs states - have recently emerged as possible microscopic candidates for single-centered black hole micro-states, as they carry zero angular momentum and appear to be robust under wall-crossing. Using the connection between quiver quantum mechanics on the Coulomb branch and the quantum mechanics of multi-centered black holes, we propose a general algorithm for reconstructing the full moduli-dependent cohomology of the moduli space of an arbitrary quiver, in terms of the BPS invariants of the pure Higgs states. We analyze many examples of quivers with loops, including all cyclic Abelian quivers and several examples with two loops or non-Abelian gauge groups, and provide supporting evidence for this proposal. We also develop methods to count pure Higgs states directly.