Chiral Phase Transition for SU(N) Gauge Theories via an Effective Lagrangian Approach

TL;DR

This paper investigates the chiral phase transition in SU(N) gauge theories using an anomaly-based effective potential, providing estimates for the critical number of flavors where chiral symmetry is restored.

Contribution

It introduces a modified effective potential that explicitly incorporates the full eta-function and anomalous dimension, extending previous models to larger N_f values.

Findings

Chiral symmetry restoration occurs when rac{ < 1.

Perturbative calculations estimate the critical flavor number N_f^c.

The approach links the phase transition to the behavior of the anomalous dimension .

Abstract

We study the chiral phase transition for vector-like SU(N) gauge theories as a function of the number of quark flavors N_f by making use of an anomaly-induced effective potential. We modify an effective potential of a previous work, suggested for N_f < N, and apply it to larger values of N_f where the phase transition is expected to occur. The new effective potential depends explicitly on the full \beta-function and the anomalous dimension \gamma of the quark mass operator. By using this potential we argue that chiral symmetry is restored for \gamma <1. A perturbative computation of \gamma then leads to an estimate of the critical value N_f^c for the transition.