Exponential Networks, WKB and Topological String
We propose a connection between 3d-5d exponential networks and exact WKB for difference equations associated to five-dimensional Seiberg-Witten curves, or equivalently, to quantum mirror curves to toric Calabi-Yau threefolds : the singularities in the Borel planes of local solutions to such differen...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2023 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2023
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212020 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Exponential Networks, WKB and Topological String. Alba Grassi, Qianyu Hao and Andrew Neitzke. SIGMA 19 (2023), 064, 44 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862705401837912064 |
|---|---|
| author | Grassi, Alba Hao, Qianyu Neitzke, Andrew |
| author_facet | Grassi, Alba Hao, Qianyu Neitzke, Andrew |
| citation_txt | Exponential Networks, WKB and Topological String. Alba Grassi, Qianyu Hao and Andrew Neitzke. SIGMA 19 (2023), 064, 44 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We propose a connection between 3d-5d exponential networks and exact WKB for difference equations associated to five-dimensional Seiberg-Witten curves, or equivalently, to quantum mirror curves to toric Calabi-Yau threefolds : the singularities in the Borel planes of local solutions to such difference equations correspond to central charges of 3d-5d BPS KK-modes. It follows that there should be distinguished local solutions of the difference equation in each domain of the complement of the exponential network, and these solutions jump at the walls of the network. We verify and explore this picture in two simple examples of 3d-5d systems, corresponding to taking the toric Calabi-Yau to be either ℂ³ or the resolved conifold. We provide the full list of local solutions in each sector of the Borel plane and in each domain of the complement of the exponential network, and find that local solutions in disconnected domains correspond to non-perturbative open topological string amplitudes on with insertions of branes at different positions of the toric diagram. We also study the Borel summation of the closed refined topological string free energy on and the corresponding non-perturbative effects, finding that central charges of 5d BPS KK-modes are related to the singularities in the Borel plane.
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| first_indexed | 2026-03-18T21:47:42Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212020 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-18T21:47:42Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Grassi, Alba Hao, Qianyu Neitzke, Andrew 2026-01-22T09:21:15Z 2023 Exponential Networks, WKB and Topological String. Alba Grassi, Qianyu Hao and Andrew Neitzke. SIGMA 19 (2023), 064, 44 pages 1815-0659 2020 Mathematics Subject Classification: 39A70; 40G10; 81T30; 81T60 arXiv:2201.11594 https://nasplib.isofts.kiev.ua/handle/123456789/212020 https://doi.org/10.3842/SIGMA.2023.064 We propose a connection between 3d-5d exponential networks and exact WKB for difference equations associated to five-dimensional Seiberg-Witten curves, or equivalently, to quantum mirror curves to toric Calabi-Yau threefolds : the singularities in the Borel planes of local solutions to such difference equations correspond to central charges of 3d-5d BPS KK-modes. It follows that there should be distinguished local solutions of the difference equation in each domain of the complement of the exponential network, and these solutions jump at the walls of the network. We verify and explore this picture in two simple examples of 3d-5d systems, corresponding to taking the toric Calabi-Yau to be either ℂ³ or the resolved conifold. We provide the full list of local solutions in each sector of the Borel plane and in each domain of the complement of the exponential network, and find that local solutions in disconnected domains correspond to non-perturbative open topological string amplitudes on with insertions of branes at different positions of the toric diagram. We also study the Borel summation of the closed refined topological string free energy on and the corresponding non-perturbative effects, finding that central charges of 5d BPS KK-modes are related to the singularities in the Borel plane. We would like to thank Murad Alim, Mat Bullimore, Fabrizio Del Monte, Lotte Hollands, Yakov Kononov, Pietro Longhi, Marcos Marino, Sebastian Schulz, Shamil Shakirov, Ivan Tulli, and Daniel Zhang for helpful discussions. We also thank the referees for reviewing the manuscript. The work of AN is supported by National Science Foundation grant 2005312 (DMS). The work of AG is partially supported by the Fonds National Suisse, Grant No.185723, and by the NCCR “The Mathematics of Physics” (SwissMAP). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Exponential Networks, WKB and Topological String Article published earlier |
| spellingShingle | Exponential Networks, WKB and Topological String Grassi, Alba Hao, Qianyu Neitzke, Andrew |
| title | Exponential Networks, WKB and Topological String |
| title_full | Exponential Networks, WKB and Topological String |
| title_fullStr | Exponential Networks, WKB and Topological String |
| title_full_unstemmed | Exponential Networks, WKB and Topological String |
| title_short | Exponential Networks, WKB and Topological String |
| title_sort | exponential networks, wkb and topological string |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212020 |
| work_keys_str_mv | AT grassialba exponentialnetworkswkbandtopologicalstring AT haoqianyu exponentialnetworkswkbandtopologicalstring AT neitzkeandrew exponentialnetworkswkbandtopologicalstring |