Two loop results from one loop computations and non perturbative solutions of exact evolution equations

TL;DR

This paper introduces a nonperturbative approach combining exact evolution equations with one-loop computations to approximate higher-order results, successfully reproducing two-loop beta-functions and anomalous dimensions in scalar field theory.

Contribution

It presents a novel method that uses one-loop expressions within an exact evolution framework to estimate two-loop and nonperturbative effects in quantum field theories.

Findings

Reproduces two-loop beta-function of scalar theory using one-loop computations.

Confirms the triviality bound at strong coupling.

Provides a practical approximation method for nonperturbative analysis.

Abstract

A nonperturbative method is proposed for the approximative solution of the exact evolution equation which describes the scale dependence of the effective average action. It consists of a combination of exact evolution equations for independent couplings with renormalization group improved one loop expressions of secondary couplings. Our method is illustrated by an example: We compute the beta-function of the quartic coupling lambda of an O(N) symmetric scalar field theory to order lambda^3 as well as the anomalous dimension to order lambda^2 using only one loop expressions and find agreement with the two loop perturbation theory. We also treat the case of very strong coupling and confirm the existence of a "triviality bound".