Calabi-Yau manifolds from pairs of non-compact Calabi-Yau manifolds

TL;DR

This paper introduces a novel method for constructing Calabi-Yau manifolds by pasting two non-compact Calabi-Yau manifolds, revealing similarities with Joyce manifolds used in M-theory.

Contribution

It presents a new construction approach for Calabi-Yau manifolds using pairs of non-compact examples, expanding the toolkit beyond traditional methods.

Findings

New construction method for Calabi-Yau manifolds

Observed similarities with Joyce manifolds

Potential implications for M-theory models

Abstract

Most of Calabi-Yau manifolds that have been considered by physicists are complete intersection Calabi-Yau manifolds of toric varieties or some quotients of product types. Purpose of this paper is to introduce a different and rather new kind of construction method of Calabi-Yau manifolds by pasting two non-compact Calabi-Yau manifolds. We will also in some details explain a curious and mysterious similarity with construction of some $G_2$-manifolds (also called Joyce manifolds), which are base spaces for M-theory.