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Les Houches lectures on non-perturbative topological strings
by Marcos Mariño
Submission summary
| Authors (as registered SciPost users): | Marcos Mariño |
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| Preprint Link: | https://arxiv.org/abs/2411.16211v2 (pdf) |
| Date submitted: | 2025-02-26 19:36 |
| Submitted by: | Mariño, Marcos |
| Submitted to: | SciPost Physics Lecture Notes |
| for consideration in Collection: |
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| Academic field: | Physics |
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Abstract
In these lecture notes for the Les Houches School on Quantum Geometry I give an introductory overview of non-perturbative aspects of topological string theory. After a short summary of the perturbative aspects, I first consider the non-perturbative sectors of the theory as unveiled by the theory of resurgence. I give a self-contained derivation of recent results on non-perturbative amplitudes, and I explain the conjecture relating the resurgent structure of the topological string to BPS invariants. In the second part of the lectures I introduce the topological string/spectral theory (TS/ST) correspondence, which provides a non-perturbative definition of topological string theory on toric Calabi-Yau manifolds in terms of the spectral theory of quantum mirror curves
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Report
These lecture notes offer an excellent and timely overview of the current status and modern developments in non-perturbative topological string theory, providing both a pedagogical introduction and a comprehensive perspective on recent advances in the field.
Requested changes
I have only one minor comment concerning Remark 2.4. To the best of my knowledge, the proof in [44] applies only for \epsilon_1, \epsilon_2 > 0. The convergence in the topological string phase was established prior to [44] in [arXiv:1608.02566], Proposition 3.1.
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