Tropical Mirror
We describe the tropical curves in toric varieties and define the tropical Gromov-Witten invariants. We introduce amplitudes for the higher topological quantum mechanics (HTQM) on special trees and show that the amplitudes are equal to the tropical Gromov-Witten invariants. We show that the sum over...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2024 |
| Main Authors: | , |
| 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/123456789/212348 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Tropical Mirror. Andrey Losev and Vyacheslav Lysov. SIGMA 20 (2024), 072, 48 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862644332065980416 |
|---|---|
| author | Losev, Andrey Lysov, Vyacheslav |
| author_facet | Losev, Andrey Lysov, Vyacheslav |
| citation_txt | Tropical Mirror. Andrey Losev and Vyacheslav Lysov. SIGMA 20 (2024), 072, 48 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We describe the tropical curves in toric varieties and define the tropical Gromov-Witten invariants. We introduce amplitudes for the higher topological quantum mechanics (HTQM) on special trees and show that the amplitudes are equal to the tropical Gromov-Witten invariants. We show that the sum over the amplitudes in -model HTQM equals the total amplitude in B-model HTQM, defined as a deformation of the -model HTQM by the mirror superpotential. We derived the mirror superpotentials for the toric varieties and showed that they coincide with the superpotentials in the mirror Landau-Ginzburg theory. We construct the mirror dual states to the evaluation observables in the tropical Gromov-Witten theory.
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| first_indexed | 2026-03-15T09:12:45Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212348 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T09:12:45Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Losev, Andrey Lysov, Vyacheslav 2026-02-05T09:55:00Z 2024 Tropical Mirror. Andrey Losev and Vyacheslav Lysov. SIGMA 20 (2024), 072, 48 pages 1815-0659 2020 Mathematics Subject Classification: 14J33; 14T20; 14N35; 81Q35 arXiv:2204.06896 https://nasplib.isofts.kiev.ua/handle/123456789/212348 https://doi.org/10.3842/SIGMA.2024.072 We describe the tropical curves in toric varieties and define the tropical Gromov-Witten invariants. We introduce amplitudes for the higher topological quantum mechanics (HTQM) on special trees and show that the amplitudes are equal to the tropical Gromov-Witten invariants. We show that the sum over the amplitudes in -model HTQM equals the total amplitude in B-model HTQM, defined as a deformation of the -model HTQM by the mirror superpotential. We derived the mirror superpotentials for the toric varieties and showed that they coincide with the superpotentials in the mirror Landau-Ginzburg theory. We construct the mirror dual states to the evaluation observables in the tropical Gromov-Witten theory. We are grateful to Pavel Mnev and Yasha Neiman for many discussions on the topics presented in this paper. We thank the referees for their valuable suggestions for improving our manuscript. V.L.’s work was supported by the Quantum Gravity Unit of the Okinawa Institute of Science and Technology Graduate University (OIST). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Tropical Mirror Article published earlier |
| spellingShingle | Tropical Mirror Losev, Andrey Lysov, Vyacheslav |
| title | Tropical Mirror |
| title_full | Tropical Mirror |
| title_fullStr | Tropical Mirror |
| title_full_unstemmed | Tropical Mirror |
| title_short | Tropical Mirror |
| title_sort | tropical mirror |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212348 |
| work_keys_str_mv | AT losevandrey tropicalmirror AT lysovvyacheslav tropicalmirror |