  We consider duality between type 0B string theory on $AdS_5\times S^5$ and
the planar CFT on $N$ electric D3-branes coincident with $N$ magnetic
D3-branes. It has been argued that this theory is stable up to a critical value
of the `t Hooft coupling but is unstable beyond that point. We suggest that
from the gauge theory point of view the development of instability is
associated with singularity in the dimension of the operator corresponding to
the tachyon field via the AdS/CFT map. Such singularities are common in large
$N$ theories because summation over planar graphs typically has a finite radius
of convergence. Hence we expect transitions between stability and instability
for string theories in AdS backgrounds that are dual to certain large $N$ gauge
theories: if there are tachyons for large AdS radius then they may be
stabilized by reducing the radius below a critical value of order the string
scale.
