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The
quantum tropical vertex
Pierrick Bousseau |
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Geometry & Topology 24 (2020) 1297–1379
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Abstract |
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Gross, Pandharipande and Siebert have shown that the –dimensional Kontsevich–Soibelman scattering diagrams compute certain genus-zero log Gromov–Witten invariants of log Calabi–Yau surfaces. We show that the –refined –dimensional Kontsevich–Soibelman scattering diagrams compute, after the change of variables , generating series of certain higher-genus log Gromov–Witten invariants of log Calabi–Yau surfaces. This result provides a mathematically rigorous realization of the physical derivation of the refined wall-crossing formula from topological string theory proposed by Cecotti and Vafa and, in particular, can be viewed as a nontrivial mathematical check of the connection suggested by Witten between higher-genus open A–model and Chern–Simons theory. We also prove some new BPS integrality results and propose some other BPS integrality conjectures. |
Keywords
scattering diagrams, quantum tori, Gromov–Witten invariants
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Mathematical Subject Classification 2010
Primary: 14N35
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References |
Publication
Received: 15 November 2018
Revised: 1 July 2019
Accepted: 4 September 2019
Published: 30 September 2020
Proposed: Jim Bryan
Seconded: Dan Abramovich, Richard P Thomas
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Authors |
| Pierrick Bousseau | |
| Department of Mathematics Imperial College London London United Kingdom |
Institute for Theoretical
Studies ETH Zürich Zürich Switzerland |
