A Holographic form for Wilson's RG

Abstract

An attempt is made to make precise the connection between Wilson's RG and "Holographic RG" by writing Wilson's RG in a holographic form. A functional formulation is given for the exact RG evolution of a scalar field in $d$ (flat) dimensions. It is shown that a change of variables maps the action to that for a scalar field in $Ad{S}_{d+1}$. This provides a holographic form for Wilson's RG that can be called "Holographic RG". This mapping can only be done for a specific form of the cutoff function in the Exact Renormalization Group formalism. The notion of scale and conformal invariance in the presence of a {\em finite} UV cutoff is emphasized. The discussion is primarily about the two-point function and the Gaussian fixed point. Some remarks are made about nontrivial fixed points.

48 pages

References in corpus (4)

• Exact evolution equation for the effective potential
• A Conformal Fixed-Point Equation for the Effective Average Action
• Exact Renormalization Group and Sine Gordon Theory
• Wilsonian Ward Identities

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• Determining wave equations in holographic QCD from Wilsonian renormalization group
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• Finite Cutoff CFT's and Composite Operators
• Constructing CFTs from AdS flows
• $SO(1,d+1)$ symmetry of the Exact RG equation
• Holographic RG and Exact RG in O(N) Model