Chiral Phase Transition for SU(N) Gauge Theories

TL;DR

This paper investigates the chiral phase transition in SU(N) gauge theories by analyzing an anomaly-induced effective potential, linking chiral symmetry restoration to the anomalous dimension and estimating the critical flavor number for the transition.

Contribution

It introduces a novel approach using an anomaly-induced effective potential dependent on the beta-function and anomalous dimension to study the phase transition.

Findings

Chiral symmetry is restored when the anomalous dimension b3 < 1.

The critical number of flavors Nf^c is estimated through perturbative calculations.

The approach connects the phase transition to fundamental gauge theory parameters.

Abstract

We describe the chiral phase transition for vector-like SU(N) gauge theories as a function of the number of quark flavors Nf by making use of an anomaly-induced effective potential. The 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 Nf^c for the transition.