Tau Functions from Joyce Structures
We argued in [Proc. Sympos. Pure Math., Vol. 103, American Mathematical Society, Providence, RI, 2021, 1-66, arXiv:1912.06504] that, when a certain sub-exponential growth property holds, the Donaldson-Thomas invariants of a 3-Calabi-Yau triangulated category should give rise to a geometric structure...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2024 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2024
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212780 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Tau Functions from Joyce Structures. Tom Bridgeland. SIGMA 20 (2024), 112, 26 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862730724299243520 |
|---|---|
| author | Bridgeland, Tom |
| author_facet | Bridgeland, Tom |
| citation_txt | Tau Functions from Joyce Structures. Tom Bridgeland. SIGMA 20 (2024), 112, 26 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We argued in [Proc. Sympos. Pure Math., Vol. 103, American Mathematical Society, Providence, RI, 2021, 1-66, arXiv:1912.06504] that, when a certain sub-exponential growth property holds, the Donaldson-Thomas invariants of a 3-Calabi-Yau triangulated category should give rise to a geometric structure on its space of stability conditions called a Joyce structure. In this paper, we show how to use a Joyce structure to define a generating function which we call the τ-function. When applied to the derived category of the resolved conifold, this reproduces the non-perturbative topological string partition function of [J. Differential Geom. 115 (2020), 395-435, arXiv:1703.02776]. In the case of the derived category of the Ginzburg algebra of the A2 quiver, we obtain the Painlevé I τ-function.
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| first_indexed | 2026-03-21T18:28:50Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212780 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T18:28:50Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bridgeland, Tom 2026-02-11T10:37:31Z 2024 Tau Functions from Joyce Structures. Tom Bridgeland. SIGMA 20 (2024), 112, 26 pages 1815-0659 2020 Mathematics Subject Classification: 53C26; 53C28; 53D30; 34M55; 14N35 arXiv:2303.07061 https://nasplib.isofts.kiev.ua/handle/123456789/212780 https://doi.org/10.3842/SIGMA.2024.112 We argued in [Proc. Sympos. Pure Math., Vol. 103, American Mathematical Society, Providence, RI, 2021, 1-66, arXiv:1912.06504] that, when a certain sub-exponential growth property holds, the Donaldson-Thomas invariants of a 3-Calabi-Yau triangulated category should give rise to a geometric structure on its space of stability conditions called a Joyce structure. In this paper, we show how to use a Joyce structure to define a generating function which we call the τ-function. When applied to the derived category of the resolved conifold, this reproduces the non-perturbative topological string partition function of [J. Differential Geom. 115 (2020), 395-435, arXiv:1703.02776]. In the case of the derived category of the Ginzburg algebra of the A2 quiver, we obtain the Painlevé I τ-function. The ideas presented here have evolved from discussions with many people over a long period of time. I would particularly like to thank Sergei Alexandrov, Andy Neitzke, Boris Pioline, and Jörg Teschner for sharing their insights and for patiently explaining many basic things to me. I am also very grateful for discussions and correspondence with Murad Alim, Fabrizio Del Monte, Maciej Dunajski, Lotte Hollands, Kohei Iwaki, Omar Kidwai, Dima Korotkin, Oleg Lisovyy, Lionel Mason, Ian Strachan, and Menelaos Zikidis. Finally, I thank the anonymous referees for their careful reading and useful suggestions for improvements. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Tau Functions from Joyce Structures Article published earlier |
| spellingShingle | Tau Functions from Joyce Structures Bridgeland, Tom |
| title | Tau Functions from Joyce Structures |
| title_full | Tau Functions from Joyce Structures |
| title_fullStr | Tau Functions from Joyce Structures |
| title_full_unstemmed | Tau Functions from Joyce Structures |
| title_short | Tau Functions from Joyce Structures |
| title_sort | tau functions from joyce structures |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212780 |
| work_keys_str_mv | AT bridgelandtom taufunctionsfromjoycestructures |