The flow tree formula for Donaldson-Thomas invariants of quivers with potentials

TL;DR

This paper proves a conjectured flow tree formula that simplifies the computation of Donaldson-Thomas invariants for quivers with potentials by expressing them through attractor invariants, using scattering diagram techniques.

Contribution

It establishes the flow tree formula as a method to compute DT invariants from attractor invariants, generalizing previous conjectures and connecting to scattering diagrams.

Findings

Proves the flow tree formula conjecture for quivers with potentials.

Shows how to reconstruct scattering diagrams from initial walls.

Provides a new computational approach for DT invariants.

Abstract

We prove the flow tree formula conjectured by Alexandrov and Pioline which computes Donaldson-Thomas invariants of quivers with potentials in terms of a smaller set of attractor invariants. This result is obtained as a particular case of a more general flow tree formula reconstructing a consistent scattering diagram from its initial walls.