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VARIATIONS OF BPS STRUCTURE AND A LARGE RANK LIMIT

Part of: Equations of mathematical physics and other areas of application Symplectic geometry, contact geometry Projective and enumerative geometry

Published online by Cambridge University Press:  12 March 2019

Jacopo Scalise  and
Jacopo Stoppa
Jacopo Scalise
Affiliation:
SISSA, via Bonomea 265, 34136 Trieste, Italy (jscalise@sissa.it; jstoppa@sissa.it)
Jacopo Stoppa
Affiliation:
SISSA, via Bonomea 265, 34136 Trieste, Italy (jscalise@sissa.it; jstoppa@sissa.it)
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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.

Keywords

Donaldson–Thomas theoryRiemann–Hilbert problemsGromov–Witten theory

MSC classification

Primary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants 35Q15: Riemann-Hilbert problems 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds

Information

Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 20 , Issue 1 , January 2021 , pp. 103 - 135
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Copyright
© Cambridge University Press 2019

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