From Black Holes to Quivers

TL;DR

This paper proposes a new algorithm to reconstruct the cohomology of quiver moduli spaces using BPS invariants of pure Higgs states, linking black hole microstates and quiver quantum mechanics.

Contribution

It introduces a general method to compute the cohomology of quiver moduli spaces from BPS invariants, applicable to complex quivers with loops and non-Abelian groups.

Findings

Validated the algorithm on various quivers with loops.

Provided methods for counting pure Higgs states directly.

Supported the approach with multiple examples and evidence.

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.