Borcea-Voisin Mirror Symmetry for Landau-Ginzburg models

TL;DR

This paper proves a new class of mirror symmetry results in Landau-Ginzburg models using FJRW theory, establishing isomorphisms linked to Calabi-Yau orbifolds and their Chen-Ruan cohomology.

Contribution

It demonstrates a broader FJRW isomorphism theorem that confirms mirror symmetry for new Landau-Ginzburg cases and connects birational Calabi-Yau orbifolds.

Findings

FJRW theory confirms Landau-Ginzburg/Calabi-Yau correspondence.

Established mirror symmetry for a new class of Landau-Ginzburg models.

Derived geometric applications to Chen-Ruan cohomology of Calabi-Yau orbifolds.

Abstract

FJRW theory is a formulation of physical Landau-Ginzburg models with a rich algebraic structure, rooted in enumerative geometry. As a consequence of a major physical conjecture, called the Landau-Ginzburg/Calabi-Yau correspondence, several birational morphisms of Calabi-Yau orbifolds should correspond to isomorphisms in FJRW theory. In this paper it is shown that not only does this claim prove to be the case, but is a special case of a wider FJRW isomorphism theorem, which in turn allows for a proof of mirror symmetry for a new class of cases in the Landau-Ginzburg setting. We also obtain several interesting geometric applications regarding the Chen-Ruan cohomology of certain Calabi-Yau orbifolds.