# Holographic Wilson's RG

## TL;DR

This paper extends the holographic ERG framework to scalar fields with anomalous dimensions, linking the boundary theory's anomalous dimension to the bulk scalar mass and exploring the implications for higher point functions.

## Contribution

It introduces a method to incorporate anomalous dimensions into the holographic ERG formalism, connecting boundary anomalous dimensions to bulk scalar masses.

## Key findings

- Established a relation between anomalous dimension and bulk scalar mass.
- Derived a prescription for alternative quantization with anomalous dimensions.
- Highlighted the potential for computing higher point functions in large N limit.

## Abstract

In an earlier paper (arXiv:1706.03371) a holographic form of the Exact Renormalization Group (ERG) evolution operator for a (perturbed) free scalar field (CFT) in D dimensions was formulated. It was shown to be equivalent, after a change of variables, to a free scalar field action in AdS_{D+1} space time. We attempt to extend this result to a theory where the scalar field has an anomalous dimension. Instead of the ERG evolution operator, we examine the generating functional with an infrared cutoff, and derive the prescription of alternative quantization by using the change of variables introduced in the previous paper. The anomalous dimension is thus related in the usual way to the mass of the bulk scalar field. Computation of higher point functions remains difficult in this theory, but should be tractable in the large N version.