Moduli Stabilization in the Heterotic/IIB Discretuum

We consider supersymmetric compactifications of type IIB and the weakly coupled heterotic string with G resp.H-flux and gaugino condensation in a hidden sector included. We point out that proper inclusion of the non-perturbative effects changes the Hodge structure of the allowed fluxes in type IIB significantly. In the heterotic theory it is known that, in contrast to the potential read off from dimensional reduction, the effective four-dimensional description demands for consistency a non-vanishing H^{2,1} component if a H^{3,0} component is already present balancing the condensate. The H^{2,1} component causes a non-Kahlerness of the underlying geometry whose moduli space is, however, not well-understood. We show that the occurrence of H^{2,1} might actually be avoided by using a KKLT-like two-step procedure for moduli stabilization. Independently of the H^{2,1} issue one-loop corrections to the gauge couplings were argued to cause a not well-controlled strong coupling transition. This problem can be avoided as well when the effects of world-sheet instantons are included. They will also stabilize the Kahler modulus what was accomplished by H^{2,1} before.