  The renormalization group flow of the worldvolume theory depends very much
from the number of unbroken supersymmetries. In the dual $AdS$ picture we break
supersymmetry by adding different types of BPS black holes. We argue, that this
BPS black hole causes a non-trivial renormalization group flow in the
worldvolume field theory and especially a regular horizon translates into a
non-trivial IR fixpoint. For this interpretation we have to rewrite the $AdS$
models into a flat space description with a linear dilaton vacuum. The dual
models (linear dilaton and the $AdS$ vacuum) can be seen as the different sides
of a domain wall. We discuss the cases of $AdS_3$ and $AdS_5$.
