  Conformal symmetry provides a systematic approximation to QCD in both its
perturbative and nonperturbative domains. One can use the AdS/CFT
correspondence between Anti-de Sitter space and conformal gauge theories to
obtain an analytically tractable approximation to QCD in the regime where the
QCD coupling is large and constant. For example, there is an exact
correspondence between the fifth-dimensional coordinate of AdS space and a
specific impact variable which measures the separation of the quark
constituents within the hadron in ordinary space-time. This connection allows
one to compute the analytic form of the frame-independent light-front
wavefunctions of mesons and baryons, the fundamental entities which encode
hadron properties and allow the computation of exclusive scattering amplitudes.
One can also use conformal symmetry as a template for perturbative QCD
predictions where the effects of the nonzero beta function can be
systematically included in the scale of the QCD coupling. This leads to fixing
of the renormalization scale and commensurate scale relations which relate
observables without scale or scheme ambiguity. I also discuss a number of novel
phenomenological features of QCD, including leading-twist single-spin
asymmetries, diffractive deep inelastic scattering, hard diffractive hadronic
reactions, the breakdown of the Lam-Tung relation in Drell-Yan reactions,
nuclear shadowing, non-universal antishadowing, and the unexpected effects of
direct higher-twist processes.
