CP violation by soft supersymmetry breaking terms in orbifold compactifications

The possibility of spontaneous breaking of CP symmetry by the expectation values of orbifold moduli is investigated with particular reference to CP violating phases in soft supersymmetry breaking terms. The effect of different mechanisms for stabilizing the dilaton and the form of the non-perturbative superpotential on the existence and size of these phases is studied. Non-perturbative superpotentials involving the absolute modular invariant j(T), such as may arise from F-theory compactifications, are considered.