Emerging Holography

TL;DR

This paper presents a four-dimensional method to derive AdS/CFT predictions for two-point functions, using Pade approximations, which aligns with holographic results and offers a gauge-invariant regularization approach.

Contribution

It introduces a novel four-dimensional extrapolation method that reproduces holographic predictions without relying on higher-dimensional theories.

Findings

Pade approximation matches leading order AdS/CFT predictions.

The approach naturally recovers the radial direction of AdS space.

Provides gauge-invariant regularization of higher-dimensional gauge theories.

Abstract

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 Pade approximation of the two-point function. We show that the Pade 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 Pade 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.