Joyce–Song wall crossing as an asymptotic expansion

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 and Song and of Kontsevich and Soibelman are related. We check the conjecture in many examples.