From Quantum Curves to Topological String Partition Functions - INSPIRE

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From Quantum Curves to Topological String Partition Functions

Ioana Coman
(
- DESY and
- U. Amsterdam, GRAPPA
)
,
Elli Pomoni
(
- DESY
)
,
Jörg Teschner
(
- DESY and
- Hamburg U.
)

Dec 14, 2022

48 pages

Published in:

Commun.Math.Phys. 399 (2023) 3, 1501-1548

Published: Dec 14, 2022

DOI:

10.1007/s00220-022-04579-4

reference search6 citations

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Abstract: (Springer)

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.

string: partition function
string: topological
Calabi-Yau
tau-function
moduli space: Kaehler
integrability
symmetry: mirror
differential equations

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Figures(0)

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