IR fixed points in $SU(3)$ gauge Theories

TL;DR

This paper introduces a new RG method to locate IR fixed points in lattice SU(3) gauge theories with various fermion flavors, providing a way to estimate the anomalous mass dimension at these points.

Contribution

The novel RG approach based on propagator scaling behavior allows precise identification of IR fixed points and estimation of anomalous dimensions in lattice gauge theories.

Findings

IR fixed points identified for Nf=16, 12, 8, 7

Method applicable to different fermion flavors

Estimation of anomalous mass dimension at fixed points

Abstract

We propose a novel RG method to specify the location of the IR fixed point in lattice gauge theories and apply it to the $SU(3)$ gauge theories with $N_f$ fundamental fermions. It is based on the scaling behavior of the propagator through the RG analysis with a finite IR cut-off, which we cannot remove in the conformal field theories in sharp contrast with the confining theories. The method also enables us to estimate the anomalous mass dimension in the continuum limit at the IR fixed point. We perform the program for $N_f=16, 12, 8 $ and $N_f=7$ and indeed identify the location of the IR fixed points in all cases.