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.

Variations of BPS structure and a large rank limit / Scalise, Jacopo Vittorio; Stoppa, Jacopo. - In: JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU. - ISSN 1474-7480. - 20:1(2021), pp. 103-135. [10.1017/S1474748019000136]

Variations of BPS structure and a large rank limit

Jacopo Scalise;Jacopo Stoppa
2021

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 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.
20
1
103
135
https://arxiv.org/abs/1705.08820
Scalise, Jacopo Vittorio; Stoppa, Jacopo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/87585
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