  We compute the NSVZ beta functions for N = 1 four-dimensional quiver theories
arising from D-brane probes on singularities, complete with anomalous
dimensions, for a large set of phases in the corresponding duality tree. While
these beta functions are zero for D-brane probes, they are non-zero in the
presence of fractional branes. As a result there is a non-trivial RG behavior.
We apply this running of gauge couplings to some toric singularities such as
the cones over Hirzebruch and del Pezzo surfaces. We observe the emergence in
string theory, of ``Duality Walls,'' a finite energy scale at which the number
of degrees of freedom becomes infinite, and beyond which Seiberg duality does
not proceed. We also identify certain quiver symmetries as T-duality-like
actions in the dual holographic theory.
