Chern-Simons Invariants and Heterotic Superpotentials

TL;DR

This paper introduces new methods to compute holomorphic Chern-Simons invariants in heterotic string compactifications, which are essential for understanding superpotentials, vacuum stability, and moduli stabilization.

Contribution

The authors develop explicit techniques using real bundle morphisms to calculate Chern-Simons invariants, including cases beyond the standard embedding and with non-flat bundles.

Findings

Large classes of examples with vanishing Chern-Simons superpotential

Explicit non-vanishing, fractionally quantized superpotentials for non-flat bundles

Generalization of previous Wilson line results

Abstract

The superpotential in four-dimensional heterotic effective theories contains terms arising from holomorphic Chern-Simons invariants associated to the gauge and tangent bundles of the compactification geometry. These effects are crucial for a number of key features of the theory, including vacuum stability and moduli stabilization. Despite their importance, few tools exist in the literature to compute such effects in a given heterotic vacuum. In this work we present new techniques to explicitly determine holomorphic Chern-Simons invariants in heterotic string compactifications. The key technical ingredient in our computations are real bundle morphisms between the gauge and tangent bundles. We find that there are large classes of examples, beyond the standard embedding, where the Chern-Simons superpotential vanishes. We also provide explicit examples for non-flat bundles where it is non-vanishing and fractionally quantized, generalizing previous results for Wilson lines.