Extension Bundles and the Standard Model

TL;DR

This paper introduces a new class of stable vector bundles on elliptically fibered Calabi-Yau threefolds, enabling the derivation of the Standard Model fermionic content from heterotic string compactifications.

Contribution

It constructs rank five vector bundles invariant under a free involution, facilitating Standard Model gauge group realization with three generations in heterotic string theory.

Findings

Constructed stable rank five bundles suitable for heterotic compactifications.

Achieved Standard Model gauge group with three generations using Wilson lines.

Provided a new geometric framework for deriving Standard Model matter content.

Abstract

We construct a new class of stable vector bundles suitable for heterotic string compactifications. Using these we describe a novel way to derive the fermionic matter content of the Standard Model from the heterotic string. For this we compactify on an elliptically fibered Calabi-Yau threefold X with two sections, the B-fibration, a variant of the ordinary Weierstrass fibration, which allows X to carry a free involution. We construct rank five vector bundles, invariant under this involution, such that turning on a Wilson line we obtain the Standard Model gauge group and find various three generation models. This rank five bundle is derived from a stable rank four bundle that arises as an extension of bundles pulled-back from the base and twisted by suitable line bundles. We also give an account of various previous results and put the present construction into perspective.