We study a class of flat bundles, of finite rank N , which arise naturally from the Donaldson-Thomas theory of a Calabi-Yau threefold X 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 X in terms of solutions to confluent hypergeometric differential equations.

A framed symplectic sheaf on a smooth projective surface X is a torsion-free sheaf E together with a trivialization on a divisor D ⊆ X and a morphism Λ 2 E → OX satisfying some additional conditions. We construct a moduli space for framed symplectic sheaves on a surface, and present a detailed study for X = P 2 C . In this case, the moduli space is irreducible and admits an ADHM-type description and a birational proper map onto the space of framed symplectic ideal instantons.

No abstract