Spontaneous symmetry breaking with Wilson renormalization group

TL;DR

This paper investigates how spontaneous symmetry breaking occurs within the Wilson renormalization group framework, emphasizing the need for fine-tuning boundary conditions in perturbative scenarios for both global and local symmetries.

Contribution

It provides a detailed analysis of symmetry breaking conditions in the Wilson RG approach, including specific cases like Z2 symmetry and the Abelian Higgs model, highlighting the fine-tuning requirement.

Findings

Symmetry breaking requires fine-tuning of boundary conditions in perturbation theory.

Both global and local symmetries can be spontaneously broken within this framework.

Detailed examination of Z2 symmetry and Abelian Higgs model cases.

Abstract

We study the conditions under which a symmetry is spontaneously broken in the Wilson renormalization group formulation. Both for a global and local symmetry, the result is that in perturbation theory one has to perform a fine tuning of the boundary conditions for the flow of the relevant couplings. We consider in detail the discrete $Z_2$ case and the Abelian Higgs model.