Softening of SUSY flavor problem from asymptotically free bulk interactions

Recently, it was pointed out that soft masses of the supersymmetric gauge theories with extra dimensions tends 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 the asymptotic freedom. From this, we find $E_6$, $E_7$ 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 $n\ge 6$) satisfying these conditions. In 5 dimensions, there is no such condition on anomaly freedom, but the softening may not be enough.