Reaching the chiral limit in many flavor systems

TL;DR

This paper investigates the non-perturbative dynamics of SU(3) gauge theories with 8 and 12 fundamental fermions using lattice simulations, revealing conformal behavior at 12 flavors and complex phenomena at 8 flavors.

Contribution

It introduces a new Monte Carlo renormalization group technique leveraging Wilson flow and provides detailed analysis of the infrared dynamics and anomalous dimensions in multi-flavor systems.

Findings

12-flavor system shows conformal infrared fixed point

8-flavor system exhibits puzzling behavior needing further study

Predicted anomalous dimension gamma*_m = 0.32(3) at 12-flavor fixed point

Abstract

We present a brief overview of our recent lattice studies of SU(3) gauge theory with N_f = 8 and 12 fundamental fermions, including some new and yet-unpublished results. To explore relatively unfamiliar systems beyond lattice QCD, we carry out a wide variety of investigations with the goal of synthesizing the results to better understand the non-perturbative dynamics of these systems. All our findings are consistent with conformal infrared dynamics in the 12-flavor system, but with 8 flavors we observe puzzling behavior that requires further investigation. Our new Monte Carlo renormalization group technique exploits the Wilson flow to obtain more direct predictions of a 12-flavor IR fixed point. Studies of N_f = 12 bulk and finite-temperature transitions also indicate IR conformality, while our current results for the 8-flavor phase diagram do not yet provide clear signs of spontaneous chiral symmetry breaking. From the Dirac eigenvalue spectrum we extract the mass anomalous dimension gamma_m, and predict gamma*_m = 0.32(3) at the 12-flavor fixed point. The N_f = 8 system again shows interesting behavior, with a large anomalous dimension across a wide range of energy scales. We use the eigenvalue density to predict the chiral condensate, and compare this approach with direct and partially-quenched measurements.