Standard-Model Bundles on Non-Simply Connected Calabi--Yau Threefolds

TL;DR

This paper proves the existence of specific stable vector bundles on elliptically fibered Calabi-Yau threefolds with fundamental group Z2, enabling the construction of heterotic M-theory models resembling the Standard Model.

Contribution

It provides a rigorous proof of stable SU(5) bundles on non-simply connected Calabi-Yau threefolds, facilitating realistic heterotic string model building.

Findings

Existence of SU(5) bundles with Euler characteristic 3

Construction of three-family models with Standard Model gauge group

Bundles compatible with M-theory five-brane anomaly cancellation

Abstract

We give a proof of the existence of $G=SU(5)$, stable holomorphic vector bundles on elliptically fibered Calabi--Yau threefolds with fundamental group $\bbz_2$. The bundles we construct have Euler characteristic 3 and an anomaly that can be absorbed by M-theory five-branes. Such bundles provide the basis for constructing the standard model in heterotic M-theory. They are also applicable to vacua of the weakly coupled heterotic string. We explicitly present a class of three family models with gauge group $SU(3)_C\times SU(2)_L\times U(1)_Y$.