Variations of BPS structure and a large rank limit

We study a class of flat bundles, of finite rank N, which arise naturally from the Donaldson–Thomas theory of a Calabi–Yau threefold via the notion of a variation of BPS structure. We prove that in a large N limit their flat sections converge to the solutions to certain infinite-dimensional Riemann–Hilbert problems recently found by Bridgeland. In particular this implies an expression for the positive degree, genus 0 Gopakumar–Vafa contribution to the Gromov–Witten partition function of in terms of solutions to confluent hypergeometric differential equations.