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Tropical Mirror

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arxiv 2204.06896 v3 pith:H6PNHYMP submitted 2022-04-14 hep-th math-phmath.MP

Andrey Losev , Vyacheslav Lysov This is my paper · ORCID
classification hep-thmath-phmath.MP
keywords mirrortropicalhtqmamplitudesgromov-witteninvariantsmodelsuperpotentials
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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.

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Cited by 1 Pith paper

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  1. Advancements in Functorial Homological Mirror Symmetry

    hep-th 2025-02 reject novelty 4.0 of 10

    A programmatic review asserting that stability and transversality in Donaldson-Thomas degeneracy formulas correspond to abelian versus nonabelian gauging in Rozansky-Witten theory, without providing a derivation.

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