Stabilizing the Complex Structure in Heterotic Calabi-Yau Vacua

TL;DR

The paper identifies a mechanism by which gauge fields in heterotic Calabi-Yau compactifications can stabilize complex-structure moduli while preserving a Minkowski vacuum. It develops this through ten-dimensional and four-dimensional field theory analyses and an algebraic-geometric Atiyah-class viewpoint, and demonstrates the mechanism with a concrete explicit example showing sizable moduli stabilization. The authors also discuss embedding the mechanism in realistic heterotic vacua via hidden-sector bundles, anomaly cancellation constraints, and non-perturbative effects, pointing toward the potential for full geometric moduli stabilization in Minkowski vacua. If realized, this approach could offer a viable route to fixing the complex-structure sector without spoiling visible-sector phenomenology.

Abstract

In this paper, we show that the presence of gauge fields in heterotic Calabi-Yau compacitifications causes the stabilisation of some, or all, of the complex structure moduli of the Calabi-Yau manifold while maintaining a Minkowski vacuum. Certain deformations of the Calabi-Yau complex structure, with all other moduli held fixed, can lead to the gauge bundle becoming non-holomorphic and, hence, non-supersymmetric. This leads to an F-term potential which stabilizes the corresponding complex structure moduli. We use 10- and 4-dimensional field theory arguments as well as a derivation based purely on algebraic geometry to show that this picture is indeed correct. An explicit example is presented in which a large subset of complex structure moduli is fixed. We demonstrate that this type of theory can serve as the hidden sector in heterotic vacua and can co-exist with realistic particle physics.