From Quantum Curves to Topological String Partition Functions

Ioana Coman; Elli Pomoni; Jörg Teschner

doi:10.1007/s00220-022-04579-4

From Quantum Curves to Topological String Partition Functions

Commun Math Phys. 2023;399(3):1501-1548. doi: 10.1007/s00220-022-04579-4. Epub 2022 Dec 14.

Authors

Ioana Coman^{1

2}, Elli Pomoni¹, Jörg Teschner^{1

3}

Affiliations

¹ Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 20607 Hamburg, Germany.
² Institute of Physics, University of Amsterdam, 1098 XH Amsterdam, The Netherlands.
³ Department of Mathematics, University of Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany.

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.