Back-reaction of the vacuum and the renormalization group flow from the conformal fixed point

We consider the GUT-like model with two scalar fields which has infinitesimal deviation from the conformal invariant fixed point in the high-energy region. In this case the dominant quantum effect is the conformal trace anomaly and the interaction between the anomaly-generated propagating conformal factor of the metric and the usual dimensional scalar field. This interaction leads to the renormalization group Row from the conformal point. In the supersymmetric conformal invariant model such an effect produces a very weak violation of supersymmetry at lower energies.