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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2024 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2024
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212780 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Tau Functions from Joyce Structures. Tom Bridgeland. SIGMA 20 (2024), 112, 26 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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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| ISSN: | 1815-0659 |