Perturbative and non-perturbative aspects of the proper time renormalization group

TL;DR

This paper investigates the proper time renormalization group flow in scalar theories, highlighting its limitations in perturbative calculations and proposing modifications to improve its accuracy for beta functions and anomalous dimensions.

Contribution

It analyzes the perturbative and non-perturbative aspects of the proper time RG, showing how to extract correct results and proposing a modified flow equation with a more general regulator.

Findings

Standard perturbative analysis does not yield correct beta and eta.

Correct beta and eta can be extracted in a specific infrared limit.

Modified flow equations with general regulators improve accuracy.

Abstract

The renormalization group flow equation obtained by means of a proper time regulator is used to calculate the two loop beta function and anomalous dimension eta of the field for the O(N) symmetric scalar theory. The standard perturbative analysis of the flow equation does not yield the correct results for both beta and eta. We also show that it is still possible to extract the correct beta and eta from the flow equation in a particular limit of the infrared scale. A modification of the derivation of the Exact Renormalization Group flow, which involves a more general class of regulators, to recover the proper time renormalization group flow is analyzed.