Improving the continuum limit of gradient flow step scaling

Abstract

We introduce a non-perturbative improvement for the renormalization group step scaling function based on the gradient flow running coupling, which may be applied to any lattice gauge theory of interest. Considering first SU(3) gauge theory with N f = 4 massless staggered fermions, we demonstrate that this improvement can remove $ \mathcal{O}\left( {{a^2}} \right) $ lattice artifacts, and thereby increases our control over the continuum extrapolation. Turning to the 12-flavor system, we observe an infrared fixed point in the infinite-volume continuum limit. Applying our proposed improvement reinforces this conclusion by removing all observable $ \mathcal{O}\left( {{a^2}} \right) $ effects. For the finite-volume gradient flow renormalization scheme defined by $ c={{{\sqrt{8t }}} \left/ {L=0.2 } \right.} $ , we find the continuum conformal fixed point to be located at $ g_{\star}^2=6.2(2) $ .