Tropical Mirror
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Published:2024-08-04
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ISSN:1815-0659
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Container-title:Symmetry, Integrability and Geometry: Methods and Applications
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Short-container-title:SIGMA
Author:
Losev Andrey, ,Lysov Vyacheslav,
Abstract
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 $A$-model HTQM equals the total amplitude in B-model HTQM, defined as a deformation of the $A$-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.
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)