Tropical Mirror
High Energy Physics - Theory
2024-08-06 v3 Mathematical Physics
math.MP
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 -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.
Cite
@article{arxiv.2204.06896,
title = {Tropical Mirror},
author = {Andrey Losev and Vyacheslav Lysov},
journal= {arXiv preprint arXiv:2204.06896},
year = {2024}
}