Heterotic Strings on Generalized Calabi-Yau Manifolds and Kaehler Moduli Stabilization

TL;DR

This paper explores heterotic string compactifications on generalized Calabi-Yau manifolds, analyzing flux quantization, moduli stabilization, and the impact of geometric torsion, with implications for supersymmetric vacua and gauge couplings.

Contribution

It extends previous work on half-flat manifolds to general cases, clarifies flux quantization, and discusses limitations in stabilizing all moduli with geometric fluxes.

Findings

Only axions from non-harmonic directions can be stabilized by torsion.

No supersymmetric extrema exist when certain cohomology groups are non-trivial.

Threshold corrections may resolve stabilization and supersymmetry issues.

Abstract

Compactifications of heterotic string theory on Generalized Calabi-Yau manifolds have been expected to give the same type of flexibility that type IIB compactifications on Calabi-Yau orientifolds have. In this note we generalize the work done on half-flat manifolds by other authors, to show how flux quantization occurs in the general case, by starting with a basis of harmonic forms and then extending it. However it turns out that only the axions associated with the non-harmonic directions in the space of Kaehler moduli, can be stabilized by the geometric (torsion) terms. Also we argue that there are no supersymmetric extrema of the potential when the second (and fourth) cohomology groups on the manifold are non-trivial. We suggest that threshold corrections to the classical gauge coupling function could solve these problems.