Nuclear Physics B (Nov 2017)

A holographic form for Wilson's RG

  • B. Sathiapalan,
  • H. Sonoda

DOI
https://doi.org/10.1016/j.nuclphysb.2017.09.018
Journal volume & issue
Vol. 924, no. C
pp. 603 – 642

Abstract

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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 AdSd+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 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.