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 γ_{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 γ_{N}=0.05(5).
Highlights
Introduction.—Conformal field theories describe a number of important physical systems
Monte Carlo renormalization group (MCRG) in particular is exact and nonperturbative, but conventional approaches are limited by the requirement of matching ensembles over large, discrete changes in scale
Significant recent work has gone into exploring the connections between Gradient flow (GF) and renormalization group (RG) [16,17,18,19,20,21,22]
Summary
Introduction.—Conformal field theories describe a number of important physical systems. Nonperturbative techniques to obtain the spectrum of operator dimensions are essential to study the full range of strongly-coupled conformal field theories. Under an RG transformation that changes the lattice cutoff as a → a0 1⁄4 ba, b > 1, the couplings transform with their corresponding scaling dimensions, and the two-point correlation function of O at distance x0 ≫ a0 1⁄4 ba transforms as [40,41]
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