The renormalization group improved effective potential in massless models

TL;DR

This paper applies renormalization group techniques to sum the effective potential in massless scalar models, revealing how the potential depends on the background field and fixing it under certain conditions, with extensions to scalar electrodynamics.

Contribution

It introduces a novel approach to summing the effective potential in massless models using RG equations, providing explicit forms and fixing the potential with vacuum conditions.

Findings

The effective potential can be summed using RG equations in massless models.

The potential becomes independent of the background field under certain conditions.

Extension of the method to massless scalar electrodynamics is demonstrated.

Abstract

The effective potential $V$ is considered in massless $\lambda\phi^4_4$ theory. The expansion of $V$ in powers of the coupling $\lambda$ and of the logarithm of the background field $\phi$ is reorganized in two ways; first as a series in $\lambda$ alone, then as a series in $\ln\phi$ alone. By applying the renormalization group (RG) equation to $V$, these expansions can be summed. Using the condition $V^\prime(v) = 0$ (where $v$ is the vacuum expectation value of $\phi$) in conjunction with the expansion of $V$ in powers of $\ln\phi$ fixes $V$ provided $v\neq 0$. In this case, the dependence of $V$ on $\phi$ drops out and $V$ is not analytic in $\lambda$. Massless scalar electrodynamics is considered using the same approach.