Lattice Study of Conformal Behavior in SU(3) Yang-Mills Theories

TL;DR

This study uses lattice simulations to explore the conformal window in SU(3) gauge theories with varying fermion flavors, identifying the transition point between conformal and confining behaviors.

Contribution

It provides detailed lattice analysis confirming the conformal behavior at N_f=12 and confinement at N_f=8, narrowing down the conformal window for SU(3) theories.

Findings

N_f=12 theory is conformal with an infrared fixed point

N_f=8 theory exhibits confinement and chiral symmetry breaking

The conformal window boundary is between N_f=8 and N_f=12

Abstract

Using lattice simulations, we study the extent of the conformal window for an SU(3) gauge theory with N_f Dirac fermions in the fundamental representation. We extend our recently reported work, describing the general framework and the lattice simulations in more detail. We find that the theory is conformal in the infrared for N_f = 12, governed by an infrared fixed point, whereas the N_f = 8 theory exhibits confinement and chiral symmetry breaking. We therefore conclude that the low end of the conformal window N_f^c lies in the range 8 <= N_f^c <= 12. We discuss open questions and the potential relevance of the present work to physics beyond the standard model.