Moduli Stabilization in the Heterotic/IIB Discretuum

TL;DR

The paper develops a detailed comparison of moduli stabilization in type IIB and heterotic flux compactifications with non-perturbative corrections. It shows that non-perturbative effects modify the allowed flux Hodge types, typically introducing $H^{2,1}$ in the heterotic case or IASD components in IIB, unless a KKLT-like two-step stabilization is used. It then demonstrates that including world-sheet instantons or a non-perturbative size-fixing superpotential can stabilize the dilaton and radial moduli at weak coupling while avoiding problematic strong-coupling transitions. The results establish a framework for constructing stabilized vacua in the heterotic/IIB discretuum with controlled fluxes and clear guidance on when to apply two-step procedures. Overall, the work connects IIB and heterotic stabilization strategies, offering concrete mechanisms to achieve robust, lower-energy vacua in a richly structured string landscape.

Abstract

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.