Heterotic Bundles on Calabi-Yau Manifolds with Small Picard Number

TL;DR

This paper systematically constructs and analyzes vector bundles on Calabi-Yau three-folds with small Picard number, identifying models suitable for heterotic string compactification with three families of matter.

Contribution

It introduces a method to construct positive rank five monad bundles on Calabi-Yau hypersurfaces with small Picard number, finding approximately 2000 models with potential physical relevance.

Findings

Constructed positive rank five monad bundles on Calabi-Yau hypersurfaces.

Identified models that can produce three families of matter.

Found about 2000 physically interesting models on two manifolds.

Abstract

We undertake a systematic scan of vector bundles over spaces from the largest database of known Calabi-Yau three-folds, in the context of heterotic string compactification. Specifically, we construct positive rank five monad bundles over Calabi-Yau hypersurfaces in toric varieties, with the number of Kahler moduli equal to one, two, and three and extract physically interesting models. We select models which can lead to three families of matter after dividing by a freely-acting discrete symmetry and including Wilson lines. About 2000 such models on two manifolds are found.