Invariant Bundles on $B$-fibered Calabi-Yau Spaces and the Standard Model

TL;DR

This paper constructs heterotic string models on special Calabi-Yau threefolds to derive the Standard Model gauge group and chiral fermions, using invariant bundles and Wilson lines.

Contribution

It introduces a method to construct stable, invariant SU(4)×U(1) bundles on B-fibered Calabi-Yau spaces, enabling realistic Standard Model features.

Findings

Successfully derives Standard Model gauge group from heterotic string.

Constructs invariant bundles using a modified spectral cover approach.

Provides a framework for realistic string compactifications on B-fibered Calabi-Yau spaces.

Abstract

We derive the Standard model gauge group together with chiral fermion generations from the heterotic string by turning on a Wilson line on a non-simply connected Calabi-Yau threefold with an SU(5) gauge group. For this we construct stable ${\bf Z_2}$-invariant $SU(4)\times U(1)$ bundles on an elliptically fibered cover Calabi-Yau threefold of special fibration type (the $B$-fibration). The construction makes use of a modified spectral cover approach giving just invariant bundles.