  Holographic CFTs admit a dual emergent description in terms of semiclassical
general relativity minimally coupled to matter fields. While the gravitational
interactions are required to be suppressed by the Planck scale, the matter
sector is allowed to interact strongly at the AdS scale. From the perspective
of the dual CFT, this requires breaking large-$N$ factorization in certain
sectors of the theory. Exactly marginal multi-trace deformations are capable of
achieving this while still preserving a consistent large-$N$ limit. We probe
the effect of these deformations on the bulk theory by computing the relevant
four-point functions in conformal perturbation theory. We find a simple answer
in terms of a finite sum of conformal blocks, indicating that the correlators
display no bulk-point singularities. This implies that the matter of the bulk
theory is made strongly coupled by boundary terms rather than local bulk
interactions. Our results suggest that holographic CFTs that describe strongly
coupled AdS matter must be isolated points on the CFT landscape or sit
infinitely far away on the conformal manifold from conventional holographic
CFTs.
