Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 22 (2026), 039, 38 pages      arXiv:2309.12046      https://doi.org/10.3842/SIGMA.2026.039

Non-Perturbative Real Topological Strings

Marcos Mariño and Maximilian Schwick
Département de Physique Théorique et Section de Mathématiques, Université de Genève, Genève, 1211, Switzerland

Received September 11, 2025, in final form March 23, 2026; Published online April 20, 2026

Abstract
We study the resurgent structure of Walcher's real topological string on general Calabi-Yau manifolds. We find trans-series solutions to the corresponding holomorphic anomaly equations, at all orders in the string coupling constant, by extending the operator formalism of the closed topological string, and we obtain explicit formulae for multi-instanton amplitudes. We find that the integer invariants counting disks appear as Stokes constants in the resurgent structure, and we provide experimental evidence for our results in the case of the real topological string on local $\mathbb{P}^2$.

Key words: resurgence; topological string theory; real topological string; Stokes constants; GV invariants; trans-series.

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