The non-perturbative topological string: from resurgence to wall-crossing of DT invariants

Abstract

We study the resurgence structure of the topological string partition function, with an emphasis on the Borel analysis of the instanton amplitudes. To this end, we introduce a differential operator that implements the pointed alien derivative when acting on the topological string partition function and its iterated alien derivatives. We show that the algebra of alien derivatives is isomorphic to the Kontsevich-Soibelman Lie algebra, thus establishing a direct link between the resurgence of the topological string and wall-crossing of generalized Donaldson-Thomas invariants. Numerically, we continue the exploration of the Borel plane of the quintic and local ℙ². For the latter, we identify Borel singularities due to bound states involving D4-branes, and match the associated Stokes constants to the appropriate Donaldson-Thomas invariants. Finally, we identify the manifestation of a D2-brane decay in the Borel plane, and match to theoretical predictions.

A non-perturbative topological persistence theorem for normally hyperbolic invariant manifolds
Wojciech Spólnik, Maciej J. Capiński
arXiv26 Oct 2026PreprintCC BY 4.0Full textDynamical systemsarXiv
Smooth and Topological Nonorientable Four-Genera of Low-Crossing Knots
Seong-Jin Lee
arXiv3 Nov 2026PreprintCC BY 4.0Full textGeometry & topologyarXiv
From samples to shape: a finite approach to topological invariants
Pedro J. Chocano
arXiv28 Sep 2026PreprintarXiv licenceFull textGeometry & topologyarXiv
Topological line arrangements and their topological invariants
Sakumi Sugawara
arXiv17 Sep 2026PreprintarXiv licenceFull textCombinatorics & discrete mathematics Geometry & topologyarXiv
Modularity of resurgent topological string
Gengbei Guo, Jiashen Chen, Jie Gu
arXiv19 Sep 2026PreprintarXiv licenceFull textMathematical physics High-energy & particle physicsarXiv

Cite

BibTeX RIS

BibTeX

@article{douaud2026nonperturbative,
  title = {{The non-perturbative topological string: from resurgence to wall-crossing of DT invariants}},
  author = {Simon Douaud and Amir-Kian Kashani-Poor},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = aug,
  doi = {10.1007/jhep08(2026)041},
  eprint = {2604.19731},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05607149v1},
  note = {CC BY 4.0},
}

RIS

TY  - JOUR
TI  - The non-perturbative topological string: from resurgence to wall-crossing of DT invariants
AU  - Simon Douaud
AU  - Amir-Kian Kashani-Poor
PY  - 2026
DA  - 2026/08/06
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep08(2026)041
UR  - https://hal.science/hal-05607149v1
AB  - We study the resurgence structure of the topological string partition function, with an emphasis on the Borel analysis of the instanton amplitudes. To this end, we introduce a differential operator that implements the pointed alien derivative when acting on the topological string partition function and its iterated alien derivatives. We show that the algebra of alien derivatives is isomorphic to the Kontsevich-Soibelman Lie algebra, thus establishing a direct link between the resurgence of the topological string and wall-crossing of generalized Donaldson-Thomas invariants. Numerically, we continue the exploration of the Borel plane of the quintic and local ℙ^2. For the latter, we identify Borel singularities due to bound states involving D4-branes, and match the associated Stokes constants to the appropriate Donaldson-Thomas invariants. Finally, we identify the manifestation of a D2-brane decay in the Borel plane, and match to theoretical predictions.
SN  - 1126-6708
SN  - 1029-8479
ER  -

Abstract

Related

Cite