  We present general methods to study the effect of multitrace deformations in
conformal theories admitting holographic duals in Anti de Sitter space. In
particular, we analyse the case that these deformations introduce an
instability both in the bulk AdS space and in the boundary CFT. We also argue
that multitrace deformations of the O(N) linear sigma model in three dimensions
correspond to nontrivial time-dependent backgrounds in certain theories of
infinitely many interacting massless fields on AdS_4, proposed years ago by
Fradkin and Vasiliev. We point out that the phase diagram of a truly marginal
large-N deformation has an infrared limit in which only an O(N) singlet field
survives. We draw from this case lessons on the full string-theoretical
interpretation of instabilities of the dual boundary theory and exhibit a toy
model that resolves the instability of the O(N) model, generated by a marginal
multitrace deformation. The resolution suggests that the instability may not
survive in an appropriate UV completion of the CFT.
