Emerging Holography

We rederive AdS/CFT predictions for infrared two-point functions by an entirely four dimensional approach, without reference to holography. This approach, originally due to Migdal in the context of QCD, utilizes an extrapolation from the ultraviolet to the infrared using a Padé approximation of the two-point function. We show that the Padé approximation and AdS/CFT give the same leading order predictions, and discuss including power corrections such as those due to condensates of gluons and quarks in QCD. At finite order the Padé approximation provides a gauge invariant regularization of a higher dimensional gauge theory in the spirit of deconstructed extra dimensions. The radial direction of anti-de Sitter space emerges naturally in this approach.