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arXiv · 1811.01978

From quantum curves to topological string partition functions

Ioana Coman·Elli Pomoni·Jörg Teschner
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Abstract

This paper describes the reconstruction of the topological string partition function for certain local Calabi-Yau (CY) manifolds from the quantum curve, an ordinary differential equation obtained by quantising their defining equations. Quantum curves are characterised as solutions to a Riemann-Hilbert problem. The isomonodromic tau-functions associated to these Riemann-Hilbert problems admit a family of natural normalisations labelled by the chambers in the extended Kähler moduli space of the local CY under consideration. The corresponding isomonodromic tau-functions admit a series expansion of generalised theta series type from which one can extract the topological string partition functions for each chamber.

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Ioana Coman, Elli Pomoni, Jörg Teschner. 2020-09-22. From quantum curves to topological string partition functions. https://arxiv.org/abs/1811.01978

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