Improved Lattice Renormalization Group Techniques

TL;DR

This paper introduces an improved non-perturbative lattice technique to compute the step-scaling function in SU(3) gauge theory with 12 massless fermions, providing evidence for an infrared fixed point.

Contribution

It develops a Wilson-flow-optimized Monte Carlo RG method with new ensembles to accurately determine the discrete beta function and IR fixed point in 12-flavor SU(3) gauge theory.

Findings

Evidence for an IR fixed point across multiple volumes and schemes.

Consistent results indicating conformal behavior in the studied theory.

Optimized Wilson flow enhances the precision of RG flow measurements.

Abstract

We compute the bare step-scaling function $s_b$ for SU(3) lattice gauge theory with $N_f = 12$ massless fundamental fermions, using the non-perturbative Wilson-flow-optimized Monte Carlo Renormalization Group two-lattice matching technique. We use a short Wilson flow to approach the renormalized trajectory before beginning RG blocking steps. By optimizing the length of the Wilson flow, we are able to determine an $s_b$ corresponding to a unique discrete $\beta$ function, after a few blocking steps. We carry out this study using new ensembles of 12-flavor gauge configurations generated with exactly massless fermions, using volumes up to $32^4$. The results are consistent with the existence of an infrared fixed point (IRFP) for all investigated lattice volumes and number of blocking steps. We also compare different renormalization schemes, each of which indicates an IRFP at a slightly different value of the bare coupling, as expected for an IR-conformal theory.