  4D Lorentzian conformal field theory (CFT) is mapped into 5D anti-de Sitter
spacetime (AdS), from the viewpoint of "geometrizing" conformal current
algebra. A large-N expansion of the CFT is shown to lead to (infinitely many)
weakly coupled AdS particles, in one-to-one correspondence with
minimal-color-singlet CFT primary operators. If all but a finite number of
"protected" primary operators have very large scaling dimensions, it is shown
that there exists a low-AdS-curvature effective field theory regime for the
corresponding finite set of AdS particles. Effective 5D gauge theory and
General Relativity on AdS are derived in this way from the most robust examples
of protected CFT primaries, Noether currents of global symmetries and the
energy-momentum tensor. Witten's prescription for computing CFT local operator
correlators within the AdS dual is derived. The main new contribution is the
derivation of 5D locality of AdS couplings. This is accomplished by studying a
confining IR-deformation of the CFT in the large-N "planar" approximation,
where the discrete spectrum and existence of an S-matrix allow the constraints
of unitarity and crossing symmetry to be solved (in standard fashion) by a
tree-level expansion in terms of 4D local "glueball" couplings. When the
deformation is carefully removed, this 4D locality (with plausible technical
assumptions specifying its precise nature) combines with the restored conformal
symmetry to yield 5D AdS locality. The sense in which AdS/CFT duality
illustrates the possibility of emergent relativity, and the special role of
strong coupling, are briefly discussed. Care is taken to conclude each step
with well-defined mathematical expressions and convergent integrals.
