Resurgent Structure of the Topological String and the First Painlevé Equation
We present an explicit formula for the Stokes automorphism acting on the topological string partition function. When written in terms of the dual partition function, our formula implies that flat coordinates in topological string theory transform as quantum periods, according to the Delabaere-Dillin...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212167 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Resurgent Structure of the Topological String and the First Painlevé Equation. Kohei Iwaki and Marcos Mariño. SIGMA 20 (2024), 028, 21 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862672540835512320 |
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| author | Iwaki, Kohei Mariño, Marcos |
| author_facet | Iwaki, Kohei Mariño, Marcos |
| citation_txt | Resurgent Structure of the Topological String and the First Painlevé Equation. Kohei Iwaki and Marcos Mariño. SIGMA 20 (2024), 028, 21 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We present an explicit formula for the Stokes automorphism acting on the topological string partition function. When written in terms of the dual partition function, our formula implies that flat coordinates in topological string theory transform as quantum periods, according to the Delabaere-Dillinger-Pham formula. We first show how the formula follows from the non-linear Stokes phenomenon of the Painlevé I equation, together with the connection between its τ-function and topological strings on elliptic curves. Then, we show that this formula is also a consequence of a recent conjecture on the resurgent structure of the topological string, based on the holomorphic anomaly equations, and it is in fact valid for arbitrary Calabi-Yau threefolds.
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| first_indexed | 2026-03-16T17:02:51Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212167 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-16T17:02:51Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Iwaki, Kohei Mariño, Marcos 2026-01-30T08:16:58Z 2024 Resurgent Structure of the Topological String and the First Painlevé Equation. Kohei Iwaki and Marcos Mariño. SIGMA 20 (2024), 028, 21 pages 1815-0659 2020 Mathematics Subject Classification: 81T45; 14N35; 34M40; 34M55 arXiv:2307.02080 https://nasplib.isofts.kiev.ua/handle/123456789/212167 https://doi.org/10.3842/SIGMA.2024.028 We present an explicit formula for the Stokes automorphism acting on the topological string partition function. When written in terms of the dual partition function, our formula implies that flat coordinates in topological string theory transform as quantum periods, according to the Delabaere-Dillinger-Pham formula. We first show how the formula follows from the non-linear Stokes phenomenon of the Painlevé I equation, together with the connection between its τ-function and topological strings on elliptic curves. Then, we show that this formula is also a consequence of a recent conjecture on the resurgent structure of the topological string, based on the holomorphic anomaly equations, and it is in fact valid for arbitrary Calabi-Yau threefolds. We would like to thank Ioana Coman, Fabrizio del Monte, Alba Grassi, Paolo Gregori, Jie Gu, Shinobu Hosono, Omar Kidwai, Oleg Lisovyy, Pietro Longhi, Kento Osuga, Boris Pioline, Ricardo Schiappa, Masa-Hiko Saito, Maximilian Schwick, Atsushi Takahashi, Yoshitugu Takei, and Joerg Teschner for useful conversations. We would also like to thank Maxim Kontsevich and Yan Soibelman for organizing the IHES school “Wall-crossing structures, analyticity and resurgence”, which made this collaboration. The work of K.I has been supported by the JSPS KAKENHI Grand Numbers 20K14323, 21K18576, 21H04994, 22H00094, 23K17654. The work of M.M. has been supported in part by the ERC-SyG project “Recursive and Exact New Quantum Theory” (ReNewQuantum), which received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program, grant agreement No. 810573. Finally, we would like to thank the anonymous referees for their helpful comments that improved the quality of the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Resurgent Structure of the Topological String and the First Painlevé Equation Article published earlier |
| spellingShingle | Resurgent Structure of the Topological String and the First Painlevé Equation Iwaki, Kohei Mariño, Marcos |
| title | Resurgent Structure of the Topological String and the First Painlevé Equation |
| title_full | Resurgent Structure of the Topological String and the First Painlevé Equation |
| title_fullStr | Resurgent Structure of the Topological String and the First Painlevé Equation |
| title_full_unstemmed | Resurgent Structure of the Topological String and the First Painlevé Equation |
| title_short | Resurgent Structure of the Topological String and the First Painlevé Equation |
| title_sort | resurgent structure of the topological string and the first painlevé equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212167 |
| work_keys_str_mv | AT iwakikohei resurgentstructureofthetopologicalstringandthefirstpainleveequation AT marinomarcos resurgentstructureofthetopologicalstringandthefirstpainleveequation |