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

TL;DR

This paper introduces a new continuous real space renormalization group method using gradient flow, enabling efficient numerical studies of operator renormalization in near-conformal systems, demonstrated on SU(3) gauge theory with 12 fermions.

Contribution

It presents a novel gradient flow-based renormalization technique that avoids ensemble matching, with applications to calculating anomalous dimensions in near-conformal gauge theories.

Findings

Mass anomalous dimension $\gamma_m = 0.23(6)$ consistent with previous estimates.

First lattice calculation of nucleon anomalous dimension $\gamma_N = 0.05(5)$.

Demonstrates the effectiveness of the method in a pilot SU(3) gauge theory study.

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 $\gamma_N = 0.05(5)$.