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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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2024
ISSN:1815-0659
Hauptverfasser: Losev, Andrey, Lysov, Vyacheslav
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2024
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/212348
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren: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
Beschreibung
Zusammenfassung: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.
ISSN:1815-0659