Softening of the supersymmetry flavor problem from asymptotically free bulk interactions

Recently, it was pointed out that soft masses of the supersymmetric gauge theories with extra dimensions tend to a flavor conserving point, which is a desirable scenario in gravity mediation models. We point out that in 6D we must consider the anomaly-free condition in addition to the condition on asymptotic freedom. From this, we find that E₆, E-₇, and E ₈ are natural candidates in 6D. There is no SU(N) model, but there exist two SO(10) models and SO(2n) models (one each for each n≥6) satisfying these conditions. In five dimensions, there is no such condition on anomaly freedom, but the softening may not be enough.