Functional renormalization group study of the two-flavor linear sigma model in the presence of the axial anomaly

TL;DR

This study uses the functional renormalization group to analyze the phase structure and fixed points of a two-flavor linear sigma model with axial anomaly, revealing stability properties relevant to chiral symmetry breaking.

Contribution

It applies the FRG method to explore the impact of axial anomaly on the phase diagram of the two-flavor linear sigma model, including the search for the O(4) fixed point.

Findings

Identification of the RG flow behavior with axial anomaly.

Analysis of the stability of the O(4) fixed point.

Insights into chiral symmetry restoration and anomaly effects.

Abstract

The $SU(2)_A \times U(2)_V$-symmetric chiral linear sigma model in the presence of the axial anomaly is studied in the local-potential approximation of the Functional Renormalization Group (FRG). The renormalization group (RG) flow is investigated in a truncation which reproduces recent results for the $U(2)_A \times U(2)_V$-symmetric model in the limit of vanishing axial anomaly strength. We search for the conjectured O(4) fixed point in the presence of the $U(1)_A$ anomaly and analyze its stability properties.