Superstring theory and $\mathrm{CP}$-violating phases: Can they be related?

We investigate the possibility of large $\mathrm{CP}$-violating phases in the soft breaking terms derived in superstring models. The bounds on the electric dipole moments (EDM’s) of the electron and neutron are satisfied through cancellations occurring because of the structure of the string models. Three general classes of four-dimensional string models are considered: (i) orbifold compactifications of perturbative heterotic string theory, (ii) scenarios based on Hořava-Witten theory, and (iii) type I string models (type IIB orientifolds). Nonuniversal phases of the gaugino mass parameters greatly facilitate the necessary cancellations among the various contributions to the EDM’s; in the overall modulus limit, the gaugino masses are universal at the tree level in both the perturbative heterotic models and the Hořava-Witten scenarios, which severely restricts the allowed regions of parameter space. Nonuniversal gaugino masses do arise at one-loop in the heterotic orbifold models, providing for corners of parameter space with $\mathcal{O}\mathrm{}\left(1\right)\mathrm{}$ phases consistent with the phenomenological bounds. However, there is a possibility of nonuniversal gaugino masses at the tree level in the type I models, depending on the details of the embedding of the SM into the D-brane sectors. We find that, in a minimal model with a particular embedding of the standard model gauge group into two D-brane sectors, viable large phase solutions can be obtained over a wide range of parameter space.