SU(5) Heterotic Standard Model Bundles

TL;DR

This paper constructs stable SU(5) bundles on a specific elliptically fibered Calabi-Yau threefold, achieving three generations of Standard Model fermions and exploring solutions that can be perturbed to Strominger system solutions, advancing heterotic flux compactifications.

Contribution

It introduces a new class of invariant SU(5) bundles on elliptic Calabi-Yau threefolds with involutions, compatible with anomaly cancellation and capable of producing realistic particle generations.

Findings

Bundles admit three generations of fermions.

Some solutions can be perturbed to Strominger system solutions.

No background fivebranes needed for anomaly cancellation.

Abstract

We construct a class of stable SU(5) bundles on an elliptically fibered Calabi-Yau threefold with two sections, a variant of the ordinary Weierstrass fibration, which admits a free involution. The bundles are invariant under the involution, solve the topological constraint imposed by the heterotic anomaly equation and give three generations of Standard Model fermions after symmetry breaking by Wilson lines of the intermediate SU(5) GUT-group to the Standard Model gauge group. Among the solutions we find some which can be perturbed to solutions of the Strominger system. Thus these solutions provide a step toward the construction of phenomenologically realistic heterotic flux compactifications via non-Kahler deformations of Calabi-Yau geometries with bundles. This particular class of solutions involves a rank two hidden sector bundle and does not require background fivebranes for anomaly cancellation.