Mirror Duality in a Joyce Manifold

TL;DR

This paper demonstrates how a Joyce G_2 manifold can be used to produce a pair of Borcea-Voisin Calabi-Yau manifolds that are mirror duals, illustrating a duality in geometric structures.

Contribution

It applies a dual Calabi-Yau construction within a Joyce G_2 manifold to explicitly produce mirror pairs, linking G_2 geometry with Calabi-Yau mirror symmetry.

Findings

Produced mirror Calabi-Yau pairs from Joyce G_2 manifold

Established a geometric duality between G_2 and Calabi-Yau structures

Extended the understanding of mirror symmetry in special holonomy manifolds

Abstract

Previously the two of the authors defined a notion of dual Calabi-Yau manifolds in a G_2 manifold, and described a process to obtain them. Here we apply this process to a compact G_2 manifold, constructed by Joyce, and as a result we obtain a pair of Borcea-Voisin Calabi-Yau manifolds, which are known to be mirror duals of each other.