Determining wave equations in holographic QCD from Wilsonian renormalization group

TL;DR

This paper proposes a method to derive holographic wave equations in AdS/CFT from quantum field theory using the renormalization group, linking the extra dimension to the renormalization scale and constraining the potential near fixed points.

Contribution

It introduces a novel approach to construct the AdS/CFT correspondence from QFT via the renormalization group, explicitly deriving wave equations and potentials.

Findings

Potential in bulk equations is fully constrained near fixed points.

Demonstrated method using a 3D scalar theory with Wilson-Fisher fixed point.

Potential behavior determined by energy scalings around fixed points.

Abstract

We show a possible way to build the AdS/CFT correspondence starting from the quantum field theory side based on renormalization group approach. An extra dimension is naturally introduced in our scheme as the renomalization scale. The holographic wave equations are derived, with the potential term being determined by the QFT properties. We discover that only around the fixed point, i.e. the conformal limit, the potential in the bulk equations can be fully constrained, and upon this foundation, the correspondence is build. We demonstrate this fact using a 3D scalar theory in which, besides the trivial fixed point, there exists the Wilson-Fisher fixed point. From the energy scalings around those fixed points, we determine the behavior of the potential in the bulk equations.