The Phase Structure of an SU(N) Gauge Theory with N_f Flavors

TL;DR

The paper analyzes the chiral phase transition in SU($N$) gauge theories as the number of massless quark flavors $N_f$ varies, arguing that the transition is controlled by an infrared fixed point with coupling $\alpha_*$. Using an RG-improved ladder approach within the CJT framework, it estimates the critical flavor number $N_f^c$ (found to be around $4N$) and characterizes the transition as continuous but not a conventional second order one, with the order parameter vanishing exponentially as $\alpha_*/\alpha_c \to 1$. In the symmetric phase, no light scalar/pseudoscalar states appear near the transition, while in the broken phase all physical masses scale with a single dynamical mass $\Sigma(0)$, consistent with walking dynamics. The authors refine their estimates by incorporating higher-order contributions to the beta function and mass anomalous dimension $\gamma$, obtaining typical uncertainties of 10–20% in $N_f^c$ and discussing the limits of the ladder approximation.

Abstract

We investigate the chiral phase transition in SU(N) gauge theories as the number of quark flavors, $N_f$, is varied. We argue that the transition takes place at a large enough value of $N_f$ so that it is governed by the infrared fixed point of the $β$ function. We study the nature of the phase transition analytically and numerically, and discuss the spectrum of the theory as the critical value of $N_f$ is approached in both the symmetric and broken phases. Since the transition is governed by a conformal fixed point, there are no light excitations on the symmetric side. We extend previous work to include higher order effects by developing a renormalization group estimate of the critical coupling.