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We study the renormalization group properties of SU(3) gauge theories with N f = 8 and 12 nearlymassless fermions, using Monte Carlo Renormalization Group (MCRG) two-lattice matching techniques to predict bare step-scaling functions sb. Traditional MCRG two-lattice matching requires that the renormalization scheme be optimized for each bare lattice coupling, so that sb is a composite of many different discrete b 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, sb 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 sb obtained by combining the Wilson flow with MCRG two-lattice matching have the distinct advantage of corresponding to unique discrete b functions.

MCRG study of 8 and 12 fundamental flavors with mixed fundamental-adjoint gauge action in strong coupling