Determination of the $N_f=12$ step scaling function using M\"obius domain wall fermions

TL;DR

This paper nonperturbatively calculates the step scaling function for twelve flavors using M"obius domain wall fermions, revealing discrepancies with staggered fermion results and advancing understanding of nonperturbative gauge dynamics.

Contribution

It provides the first nonperturbative determination of the step scaling function for twelve flavors with M"obius domain wall fermions, highlighting discrepancies with staggered fermion simulations.

Findings

Consistent step scaling function across different flows and operators.

Significant discrepancy with staggered fermion simulation results.

Results support the existence of a conformal window for twelve flavors.

Abstract

We calculate the renormalized step scaling function for twelve fundamental flavors nonperturbatively by determining the gradient flow coupling on gauge field configurations generated with dynamical stout-smeared M\"obius domain wall fermions and Symanzik gauge action. Using Zeuthen, Symanzik, and Wilson flow we measure the energy density with three different operators. Our updated analysis is based on up to five volume pairs ranging from L^4=8^4 up to 32^4. Predictions for the infinite volume extrapolated step scaling function based on different flows and operators are mutually consistent. Our new results confirm the previously observed significant discrepancy with staggered fermion simulations in a wide range of the renormalized coupling.