Connecting the Holographic and Wilsonian Renormalization Groups

TL;DR

This paper establishes a direct, explicit duality between the Wilsonian renormalization group flow in a gauge theory and the holographic flow in AdS space, providing a string theory-independent AdS/CFT correspondence framework.

Contribution

It introduces a formal duality linking gauge theory couplings with AdS fields via Hubbard-Stratonovich transforms, aligning RG flow with holographic dynamics.

Findings

Wilsonian RG flow matches holographic flow in AdS.

Fields in AdS identified with transformed gauge couplings.

Framework does not depend on string theory assumptions.

Abstract

Inspired by the AdS/CFT correspondence, we develop an explicit formal duality between the planar limit of a d-dimensional gauge theory and a classical field theory in a (d+1)-dimensional anti-de Sitter space. The key ingredient is the identification of fields in AdS with generalized Hubbard-Stratonovich transforms of single-trace couplings of the QFT. We show that the Wilsonian renormalization group flow of these transformed couplings matches the holographic (Hamilton-Jacobi) flow of bulk fields along the radial direction in AdS. This result allows one to outline an AdS/CFT dictionary that does not rely on string theory.