Mirror duality of Landau-Ginzburg models via Discrete Legendre Transforms
Helge Ruddat
TL;DR
This paper introduces a duality for Landau-Ginzburg models using discrete Legendre transforms, generalizing mirror symmetry constructions and connecting to the semi-flat Strominger-Yau-Zaslow framework.
Contribution
It presents a novel duality concept for Landau-Ginzburg models based on discrete Legendre transforms, extending previous mirror symmetry methods.
Findings
Defines a new duality via discrete Legendre transforms
Links the duality to semi-flat SYZ mirror symmetry
Generalizes previous mirror constructions for toric complete intersections
Abstract
We introduce a duality of Landau-Ginzburg models based on the notion of the discrete Legendre transform given by Gross-Siebert. It generalizes the duality used to construct mirrors of complete intersections in toric varieties in a recent joint work with Gross and Katzarkov. We discuss how it appears as a limit version of the semi-flat Strominger-Yau-Zaslow construction of mirror symmetry with potential given as the obstruction in Floer theory.
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Taxonomy
TopicsGeometric and Algebraic Topology · Topological and Geometric Data Analysis · Advanced Combinatorial Mathematics