MCRG study of 8 and 12 fundamental flavors

TL;DR

This study investigates the renormalization group behavior of SU(3) gauge theories with 8 and 12 flavors using Monte Carlo Renormalization Group techniques, introducing an improved method with Wilson flow to better identify fixed points.

Contribution

An improved MCRG two-lattice matching procedure using Wilson flow that yields unique discrete beta functions for SU(3) gauge theories with multiple flavors.

Findings

12-flavor theory shows an infrared fixed point.

8-flavor theory's step-scaling function is affected by lattice artifacts.

The new method provides a clearer identification of fixed points.

Abstract

We study the renormalization group properties of SU(3) gauge theories with N_f=8 and 12 nearly-massless fermions, using Monte Carlo Renormalization Group (MCRG) two-lattice matching techniques to predict bare step-scaling functions s_b. Traditional MCRG two-lattice matching requires that the renormalization scheme be optimized for each bare lattice coupling, so that s_b is a composite of many different discrete beta functions. We propose an improved procedure that uses the Wilson flow to eliminate the need for this optimization of the RG blocking transformation. While our 12-flavor results indicate an infrared fixed point, s_b for N_f=8 is significantly different from zero until strong-coupling lattice artifacts obstruct two-lattice matching. Although both procedures produce qualitatively similar bare step-scaling functions, the new s_b obtained by combining the Wilson flow with MCRG two-lattice matching have the distinct advantage of corresponding to unique discrete beta functions.