Mathematical structures of non-perturbative topological string theory: from GW to DT invariants

M Alim, A Saha, J Teschner, I Tulli - Communications in Mathematical …, 2023 - Springer
We study the Borel summation of the Gromov–Witten potential for the resolved conifold. The
Stokes phenomena associated to this Borel summation are shown to encode the Donaldson …

Quantum curves, resurgence and exact WKB

M Alim, L Hollands, I Tulli - SIGMA. Symmetry, Integrability and Geometry …, 2023 - emis.de
We study the non-perturbative quantum geometry of the open and closed topological string
on the resolved conifold and its mirror. Our tools are finite difference equations in the open …

Topological Recursion and Uncoupled BPS Structures II: Voros Symbols and the -Function

K Iwaki, O Kidwai - Communications in Mathematical Physics, 2023 - Springer
We continue our study of the correspondence between BPS structures and topological
recursion in the uncoupled case, this time from the viewpoint of quantum curves. For spectral …

Intrinsic non-perturbative topological strings

M Alim - arXiv preprint arXiv:2102.07776, 2021 - arxiv.org
We study difference equations which are obtained from the asymptotic expansion of
topological string theory on the deformed and the resolved conifold geometries as well as for …

Difference equation for the Gromov-Witten potential of the resolved conifold

M Alim - Journal of Geometry and Physics, 2023 - Elsevier
A difference equation is proved for the Gromov-Witten potential of the resolved conifold.
Using the Gopakumar-Vafa resummation of the Gromov-Witten invariants of any Calabi-Yau …

Conformal TBA for resolved conifolds

S Alexandrov, B Pioline - Annales Henri Poincare, 2022 - Springer
Abstract We revisit the Riemann–Hilbert problem determined by Donaldson–Thomas
invariants for the resolved conifold and for other small crepant resolutions. While this …

A Hyperkähler geometry associated to the BPS structure of the resolved conifold

M Alim, A Saha, I Tulli - Journal of Geometry and Physics, 2022 - Elsevier
We associate to the resolved conifold an affine special Kähler (ASK) manifold of complex
dimension 1, and an instanton corrected hyperkähler (HK) manifold of complex dimension 2 …

Non-perturbative topological strings from resurgence

M Alim - arXiv preprint arXiv:2406.17852, 2024 - arxiv.org
The partition function of topological string theory on any family of Calabi-Yau threefolds is
defined perturbatively as an asymptotic series in the topological string coupling and …