# Heterotic Line Bundle Models on Elliptically Fibered Calabi-Yau Three-folds

## TL;DR

This paper constructs and analyzes heterotic line bundle models on elliptically fibered Calabi-Yau three-folds with specific geometric properties, identifying over 400 models with promising features for particle physics, including GUT groups and potential standard model descent.

## Contribution

It develops mathematical tools for line bundle model construction on elliptically fibered Calabi-Yau three-folds with weak Fano bases and performs a computer scan to identify viable models.

## Key findings

- Over 400 models with the right number of families and SU(5) GUT group
- Models can descend to standard-like models after Z2 quotient
- Presence of many vector-like states in the models

## Abstract

We analyze heterotic line bundle models on elliptically fibered Calabi-Yau three-folds over weak Fano bases. In order to facilitate Wilson line breaking to the standard model group, we focus on elliptically fibered three-folds with a second section and a freely-acting involution. Specifically, we consider toric weak Fano surfaces as base manifolds and identify six such manifolds with the required properties. The requisite mathematical tools for the construction of line bundle models on these spaces, including the calculation of line bundle cohomology, are developed. A computer scan leads to more than $400$ line bundle models with the right number of families and an $SU(5)$ GUT group which can descend to standard-like models after taking the $\mathbb{Z}_2$ quotient. A common and surprising feature of these models is the presence of a large number of vector-like states.