Quivers and curves in higher dimension

TL;DR

This paper establishes a deep connection between Donaldson-Thomas invariants of certain quivers and genus zero punctured Gromov-Witten invariants of holomorphic symplectic cluster varieties, using scattering diagrams and tropical geometry.

Contribution

It introduces a novel correspondence linking DT invariants and Gromov-Witten invariants through scattering diagrams and tropical geometry techniques.

Findings

Proves a correspondence between DT invariants and Gromov-Witten invariants.

Uses scattering diagrams to compare wall-crossing behaviors.

Employs tropical geometry to relate different invariants.

Abstract

We prove a correspondence between Donaldson-Thomas invariants of quivers with potential having trivial attractor invariants and genus zero punctured Gromov-Witten invariants of holomorphic symplectic cluster varieties. The proof relies on the comparison of the stability scattering diagram, describing the wall-crossing behavior of Donaldson-Thomas invariants, with a scattering diagram capturing punctured Gromov-Witten invariants via tropical geometry.