MCRG study of 8 and 12 fundamental flavors
Abstract
We study the renormalization group properties of SU(3) gauge theories with Nf=8 and 12 nearly-massless 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 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, sb for Nf=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 beta functions.
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