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arXiv · 1705.08820

Variations of BPS structure and a large rank limit

Jacopo Scalise·Jacopo Stoppa
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Abstract

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.

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Jacopo Scalise, Jacopo Stoppa. 2017-05-24. Variations of BPS structure and a large rank limit. https://doi.org/10.1017/s1474748019000136

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