Mass anomalous dimension from Dirac eigenmode scaling in conformal and confining systems

TL;DR

This paper investigates how the mass anomalous dimension, derived from Dirac eigenmode scaling, varies with energy in different SU(3) systems, revealing behaviors consistent with conformal and confining dynamics.

Contribution

It introduces a method to study the energy dependence of the mass anomalous dimension using Dirac eigenmode scaling in lattice systems with varying flavors.

Findings

For 4 flavors, gamma_m decreases with energy, aligning with perturbative predictions.

For 8 flavors, energy dependence of gamma_m is too weak to detect.

For 12 flavors, gamma_m increases with energy, indicating an infrared fixed point.

Abstract

The mode number of the Dirac operator scales with an exponent related to the mass anomalous dimension gamma_m. This relation holds both in IR-conformal systems, as well as in confining systems for large enough eigenvalues. We investigate the Nf=4, 8 and 12 flavor SU(3) systems at several couplings near the chiral limit, and show that in general the scaling exponent varies with the eigenvalue, describing the dependence of gamma_m on the energy (or, equivalently, on the running coupling). This energy dependence can be explored even with fixed lattice parameters (bare coupling and mass). We find that for the 4 flavor system the mass anomalous dimension decreases as the energy increases, consistent with perturbative expectations. For the 8 flavor system the energy dependence is too weak to be observable at present. The 12 flavor system at our strongest couplings shows the anomalous dimension increasing with energy, consistent with backward flow and the presence of an infrared fixed point. At weaker couplings we determine a preliminary value for the mass anomalous dimension of the 12 flavor system at the infrared fixed point, gamma_m^*=0.27(3).