Wilson lines and Chern-Simons flux in explicit heterotic Calabi-Yau compactifications

TL;DR

This paper investigates how Wilson lines in heterotic Calabi-Yau compactifications induce H-flux via Chern-Simons terms, affecting background consistency and moduli stabilization, with explicit computations for specific models.

Contribution

It provides a method to compute H-flux and superpotential from Wilson lines in explicit Calabi-Yau compactifications using Chern-Simons invariants.

Findings

Computed H-flux and superpotential for specific Calabi-Yau models.

Classified special Lagrangian submanifolds relevant for flux calculations.

Demonstrated the impact of Wilson lines on flux and potential moduli stabilization.

Abstract

We study to what extent Wilson lines in heterotic Calabi-Yau compactifications lead to non-trivial H-flux via Chern-Simons terms. Wilson lines are basic ingredients for Standard Model constructions but their induced H-flux may affect the consistency of the leading order background geometry and of the two-dimensional worldsheet theory. Moreover H-flux in heterotic compactifications would play an important role for moduli stabilization and could strongly constrain the supersymmetry breaking scale. We show how to compute H-flux and the corresponding superpotential, given an explicit complete intersection Calabi-Yau compactification and choice of Wilson lines. We do so by classifying special Lagrangian submanifolds in the Calabi-Yau, understanding how the Wilson lines project onto these submanifolds, and computing their Chern-Simons invariants. We illustrate our procedure with the quintic hypersurface as well as the split-bicubic, which can provide a potentially realistic three generation model.