Standard Model bundles of the heterotic string

TL;DR

This paper presents a method to construct supersymmetric three-generation Standard Model-like theories using heterotic string compactifications on specific elliptically fibered Calabi-Yau manifolds with non-trivial fundamental group.

Contribution

It introduces a construction of Standard Model bundles on non-simply-connected elliptic Calabi-Yau manifolds using spectral cover techniques and involutions.

Findings

Constructed models with three generations and Standard Model gauge group

Identified involutions on spectral data for bundle invariance

Demonstrated general constructibility of invariant bundles

Abstract

We show how to construct supersymmetric three-generation models with gauge group and matter content of the Standard Model in the framework of non-simply-connected elliptically fibered Calabi-Yau manifolds Z. The elliptic fibration on a cover Calabi-Yau, where the model has 6 generations of SU(5) and the bundle is given via the spectral cover description, has a second section leading to the needed free involution. The relevant involution on the defining spectral data of the bundle is identified for a general Calabi-Yau of this type and invariant bundles are generally constructible.