Renormalization group and effective potential: a simple non-perturbative approach

TL;DR

This paper introduces a straightforward non-perturbative method based on the Wilson renormalization group to calculate the effective potential in field theories, demonstrating its effectiveness compared to perturbative results.

Contribution

It presents a simple differential equation approach derived from the exact renormalization group, improving non-perturbative calculations of the effective potential.

Findings

The method yields a solvable differential equation for the effective potential.

Comparison shows the non-perturbative approach outperforms two-loop perturbation theory.

Application to sextic field theory demonstrates the approach's effectiveness.

Abstract

We develop a simple non-perturbative approach to the calculation of a field theory effective potential that is based on the Wilson or exact renormalization group. Our approach follows Shepard et al's idea [Phys. Rev. D51, 7017 (1995)] of converting the exact renormalization group into a self-consistent renormalization method. It yields a simple second order differential equation for the effective potential. The equation can be solved and its solution is compared with other non-perturbative results and with results of perturbation theory. In three dimensions, we are led to study the sextic field theory ($\lambda\phi^4+g\phi^6$). We work out this theory at two-loop perturbative order and find the non-perturbative approach to be superior.