On the relation between RG and ERG

TL;DR

This paper explores the connection between Wilson's exact renormalization group (ERG) and the traditional RG equations, demonstrating their emergence in phi4 theory and proposing a scheme that aligns with the MS scheme.

Contribution

It introduces a specific parameterization scheme for ERG solutions in phi4 theory and shows its RG equations are mass independent, suggesting equivalence with the MS scheme.

Findings

Parameters obey mass independent RG equations

Scheme aligns with the MS scheme for dimensional regularization

Demonstrates the emergence of RG equations from ERG in phi4 theory

Abstract

We discuss how the ordinary renormalization group (RG) equations arise in the context of Wilson's exact renormalization group (ERG) as formulated by Polchinski. We consider the phi4 theory in four dimensional euclidean space as an example, and introduce a particular scheme of parameterizing the solutions of the ERG equations. By analyzing the scalar composite operators of dimension two and four, we show that the parameters obey mass independent RG equations. We conjecture the equivalence of our parameterization scheme with the MS scheme for dimensional regularization.