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High Energy Physics - Theory

arXiv:2204.06896 (hep-th)
[Submitted on 14 Apr 2022 (v1), last revised 4 Aug 2024 (this version, v3)]

Title:Tropical Mirror

Authors:Andrey Losev, Vyacheslav Lysov
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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.
Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
Cite as: arXiv:2204.06896 [hep-th]
  (or arXiv:2204.06896v3 [hep-th] for this version)
  https://doi.org/10.48550/arXiv.2204.06896
Journal reference: SIGMA 20 (2024), 072, 48 pages
Related DOI: https://doi.org/10.3842/SIGMA.2024.072

Submission history

From: Vyacheslav Lysov [view email] [via Journal Sigma as proxy]
[v1] Thu, 14 Apr 2022 11:49:54 UTC (37 KB)
[v2] Thu, 27 Jul 2023 11:21:35 UTC (45 KB)
[v3] Sun, 4 Aug 2024 07:31:15 UTC (51 KB)
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