Joyce-Song wall-crossing as an asymptotic expansion

TL;DR

This paper proposes that the Joyce-Song wall-crossing formula for Donaldson-Thomas invariants can be derived from an asymptotic expansion in field theory, offering new insights into its relation with Kontsevich-Soibelman formula.

Contribution

It introduces a conjecture linking Joyce-Song wall-crossing to asymptotic expansions in field theory, supported by multiple example verifications.

Findings

Conjecture supported by numerous examples

Provides a new perspective on the relation between wall-crossing formulas

Suggests a natural derivation of Joyce-Song formula from field theory

Abstract

We conjecture that the Joyce-Song wall-crossing formula for Donaldson-Thomas invariants arises naturally from an asymptotic expansion in the field theoretic work of Gaiotto, Moore and Neitzke. This would also give a new perspective on how the formulae of Joyce-Song and Kontsevich-Soibelman are related. We check the conjecture in many examples.