Connecting the Holographic and Wilsonian Renormalization Groups

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.

11 pages, 1 figure; metadata modified in v2; added references and minor changes in v3; v4 as published in JHEP

References in corpus (8)

• Lectures on Holographic Superfluidity and Superconductivity
• Holography from Conformal Field Theory
• Holographic and Wilsonian Renormalization Groups
• Wilsonian Approach to Fluid/Gravity Duality
• Holographic dual of free field theory
• Holographic description of quantum field theory
• Holographic description of large N gauge theory
• Hints on integrability in the Wilsonian/holographic renormalization group

Cited by in corpus (5)

• Background independent holographic description : From matrix field theory to quantum gravity
• Wilsonian renormalisation and the exact cut-off scale from holographic duality
• Geometric encoding of renormalization group $\beta -$functions in an emergent holographic dual description
• Dimensional renormalization in AdS/CFT
• Kinematics of Horizon and Singularity and IR/UV Mixing in AdS