  We study in detail the recently-found family of asymptotically AdS$_5\times
S^5$ type IIB supergravity solutions dual to the $\mathcal{N}=1^*$ SYM theory
with equal masses. The backgrounds exhibit a naked singularity and are labelled
by a dimensionless parameter, $\lambda$, which is interpreted as the ratio of
the gaugino condensate and the mass in the dual field theory. When
$|\lambda|<1$ we show that the naked singularity is due to a smeared
distribution of polarized $(p,q)$ five-branes. For this range of parameters we
study the nature of the singularity using probe strings and show that the dual
line operators exhibit screening behavior. These features are in line with the
physics anticipated in the work of Polchinski-Strassler. For $|\lambda|=1$ the
naked singularity has qualitatively different behavior which has no clear brane
interpretation. We show that when $\lambda=1$ the singularity can be excised
and replaced by a smooth Euclidean supergravity solution with an $S^4$
boundary.
