The question of (Formula presented) violating phases and electric dipole moments (EDMs) for the electron (Formula presented) and the neutron (Formula presented) for supergravity models with nonuniversal soft breaking is considered for models with a light (Formula presented) mass spectrum and R-parity invariance. As with models with universal soft breaking (MSUGRA) one finds that a serious fine-tuning problem generally arises for (Formula presented) (the phase of the B soft breaking parameter at the GUT scale), if the experimental EDM constraints are obeyed and radiative breaking of (Formula presented) occurs. A D-brane model where (Formula presented) is associated with one set of 5-branes and (Formula presented) with another intersecting set of 5-branes is examined, and the cancellation phenomena is studied over the parameter space of the model. Large values of (Formula presented) (the phase of B at the electroweak scale) can be accommodated, though again (Formula presented) must be fine-tuned. Using the conventional prescription for calculating (Formula presented) one finds the region in parameter space where the experimental EDM constraints on both (Formula presented) and (Formula presented) hold is significantly reduced, and generally requires (Formula presented) for most of the parameter space, though there are small allowed regions even for (Formula presented) We find that the Weinberg three gluon term generally makes significant contributions, and the results are sensitive to the values of the quark masses. 2000 The American Physical Society.
