Renormalization Group Evolution of the Effective Potential in the Broken Symmetry Phase

TL;DR

This paper studies how the effective potential in a broken symmetry scalar field theory evolves under the renormalization group, revealing it follows the same RG functions as in the symmetric phase.

Contribution

It demonstrates that the RG evolution of the effective potential in the broken phase is governed by the same RG functions as in the symmetric phase, using the vacuum expectation value condition.

Findings

RG evolution in broken phase matches symmetric phase RG functions

Effective potential's RG behavior is governed by the same functions in both phases

Vacuum expectation value condition is key to this equivalence

Abstract

We investigate the renormalization group(RG) evolution for the neutral scalar field theory in the broken symmetry phase. By using the minimum condition of the vacuum expectation value(VEV), we show that the RG evlution of the effective potential in the broken symmetry phase is governed by the same RG functions in case of the symmetric phase.