Spontaneous Symmetry Breaking without classical fields: a Functional Renormalization Group approach

TL;DR

This paper introduces a novel FRG-based method to describe spontaneous symmetry breaking without relying on traditional order parameters, using the Ward ratio to distinguish phases and enabling unified potential evolution.

Contribution

It develops a new approach using the Ward ratio within FRG to characterize SSB without classical fields, compatible with Ward identities.

Findings

Unified scale evolution of the effective potential in both phases

Accelerated evolution in the critical regime

Effective description without Landau theory dependence

Abstract

We propose an approach to describe Spontaneous Symmetry Breaking (SSB) that does not rely on the order parameter dependent free energy (Landau theory). We use the Functional Renormalization Group (FRG) evolution of the explicitly broken theory, using a truncation scheme that is compatible with the Ward identities. To represent the symmetry breaking, we propose to use the "Ward ratio" which is zero in the symmetric phase and unity in the broken phase. In this approach a unified scale evolution of the effective potential is applicable in both phases. It is peculiar that the scale evolution is accelerated in the critical regime.