Quivers, flow trees, and log curves

Donaldson-Thomas (DT) invariants of a quiver with potential can be expressed in terms of simpler attractor DT invariants by a universal formula.The coefficients in this formula are calculated combinatorially using attractor flow trees.In this paper, we prove that these coefficients are genus 0 log Gromov-Witten invariants of d-dimensional toric varieties, where d is the number of vertices of the quiver.This result follows from a log-tropical correspondence theorem that relates (d-2)-dimensional families of tropical curves obtained as universal deformations of attractor flow trees, and rational log curves in toric varieties.