Heterotic strings on generalized Calabi-Yau manifolds and Kaehler moduli stabilization

Compactifications of heterotic string theory on generalized Calabi-Yau manifolds with SU(3) structure, 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.