  We discuss universal properties of conformal field theories with holographic
duals. A central feature of these theories is the existence of a low-lying
sector of operators whose correlators factorize. We demonstrate that
factorization can only hold in the large central charge limit. Using conformal
invariance and factorization we argue that these operators are naturally
represented as fields in AdS as this makes the underlying linearity of the
system manifest. In this class of CFTs the solution of the conformal bootstrap
conditions can be naturally organized in structures which coincide with Witten
diagrams in the bulk. The large value of the central charge suggests that the
theory must include a large number of new operators not captured by the
factorized sector. Consequently we may think of the AdS hologram as an
effective representation of a small sector of the CFT, which is embedded inside
a much larger Hilbert space corresponding to the black hole microstates.
