TL;DR
This paper introduces a duality construction for toric Landau-Ginzburg models that unifies and extends previous mirror symmetry constructions, applicable to complete intersections and providing resolutions for singular mirrors.
Contribution
It presents a new duality framework for toric Landau-Ginzburg models that generalizes existing mirror symmetry constructions and addresses singularities.
Findings
Reconstructs Batyrev-Borisov, Berglund-Hübsch, Givental, and Hori-Vafa models
Applicable to more general situations beyond previous models
Provides partial resolutions for singular mirrors
Abstract
We introduce a duality construction for toric Landau-Ginzburg models, applicable to complete intersections in toric varieties via the sigma model / Landau-Ginzburg model correspondence. This construction is shown to reconstruct those of Batyrev-Borisov, Berglund-H"ubsch, Givental, and Hori-Vafa. It can be done in more general situations, and provides partial resolutions when the above constructions give a singular mirror. An extended example is given: the Landau-Ginzburg models dual to elliptic curves in (P^1)^2 .
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