Nonperturbative Renormalization of Operators in Near-Conformal Systems Using Gradient Flows

Abstract

We propose a continuous real space renormalization group transformation based on gradient flow, allowing for a numerical study of renormalization without the need for costly ensemble matching. We apply our technique in a pilot study of SU$(3)$ gauge theory with $N_f=12$ fermions in the fundamental representation, finding the mass anomalous dimension to be ${\gamma }_m=0.23(6)$, consistent with other perturbative and lattice estimates. We also present the first lattice calculation of the nucleon anomalous dimension in this theory, finding ${\gamma }_N=0.05(5)$.

Comments: 5 pages, 3 figures. v2: updated references, edited derivation for clarity. v3: updated to published version