Scale-dependent mass anomalous dimension from Dirac eigenmodes

TL;DR

This paper introduces a universal lattice method to measure the scale-dependent fermion mass anomalous dimension in gauge theories, providing insights into conformal or chiral symmetry-breaking behaviors across different fermion flavors.

Contribution

The authors develop a universal approach to extract the scale-dependent mass anomalous dimension from Dirac eigenmodes applicable to various lattice models, including conformal and chirally broken systems.

Findings

Nf=4 model behaves as expected for QCD-like systems.

Nf=12 results suggest an infrared fixed point with gamma_m^*=0.32(3).

Nf=8 shows a large anomalous dimension, indicating possible conformal or walking behavior.

Abstract

We investigate the eigenmodes of the massless Dirac operator to extract the scale-dependent fermion mass anomalous dimension gamma_m(mu). By combining simulations on multiple lattice volumes, and when possible several gauge couplings, we are able to measure the anomalous dimension across a wide range of energy scales. The method that we present is universal and can be applied to any lattice model of interest, including both conformal or chirally broken systems. We consider SU(3) lattice gauge theories with Nf=4, 8 and 12 light or massless fermions. The 4-flavor model behaves as expected for a QCD-like system and demonstrates that systematic effects are manageable in practical lattice calculations. Our 12-flavor results are consistent with the existence of an infrared fixed point, at which we predict the scheme-independent mass anomalous dimension gamma_m^*=0.32(3). For the 8-flavor model we observe a large anomalous dimension across a wide range of energy scales. Further investigation is required to determine whether Nf=8 is chirally broken and walking, or if it possesses a strongly-coupled conformal fixed point.