  We study, using the dual AdS description, the vacua of field theories where
some of the gauge symmetry is broken by expectation values of scalar fields. In
such vacua, operators built out of the scalar fields acquire expectation
values, and we show how to calculate them from the behavior of perturbations to
the AdS background near the boundary. Specific examples include the ${\cal
N}=4$ SYM theory, and theories on D3 branes placed on orbifolds and conifolds.
We also clarify some subtleties of the AdS/CFT correspondence that arise in
this analysis. In particular, we explain how scalar fields in AdS space of
sufficiently negative mass-squared can be associated with CFT operators of {\it
two} possible dimensions. All dimensions are bounded from below by $(d-2)/2$;
this is the unitarity bound for scalar operators in $d$-dimensional field
theory. We further argue that the generating functional for correlators in the
theory with one choice of operator dimension is a Legendre transform of the
generating functional in the theory with the other choice.
