Functional Renormalization for Chiral and U_A(1) Symmetries at Finite Temperature

TL;DR

This paper uses the functional renormalization group to analyze chiral and U_A(1) symmetry restoration at finite temperature within the SU(3) linear sigma model, revealing simultaneous phase transitions and meson mass behaviors.

Contribution

It introduces a novel application of the functional renormalization group to study symmetry restoration and meson mass evolution at finite temperature in the SU(3) linear sigma model.

Findings

Chiral and U_A(1) symmetries restore at the same critical temperature in the chiral limit.

Goldstone theorem holds at finite temperature.

Explicit symmetry breaking leads to partial and slow restoration of symmetries.

Abstract

We investigated the chiral symmetry and U_A(1) anomaly at finite temperature by applying the functional renormalization group to the SU(3) linear sigma model. Expanding the local potential around the classical fields, we derived the flow equations for the renormalization parameters. In chiral limit, the flow equation for the chiral condensate is decoupled from the others and can be analytically solved. The Goldstone theorem is guaranteed in vacuum and at finite temperature, and the two phase transitions for the chiral and U_A(1) symmetry restoration happen at the same critical temperature. In general case with explicit chiral symmetry breaking, the two symmetries are partially and slowly restored, and the scalar and pseudoscalar meson masses are controlled by the restoration in the limit of high temperature.