Gregory Petropoulos

Scale-dependent mass anomalous dimension from Dirac eigenmodes

A bstractWe investigate the eigenmodes of the massless Dirac operator to extract the scale-dependent fermion mass anomalous dimension γm(μ). 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

Improving the continuum limit of gradient flow step scaling

\gamma_m^{*}=0.32(3)

Finite size scaling of conformal theories in the presence of a near-marginal operator

. 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.

Determining the mass anomalous dimension through the eigenmodes of Dirac operator

A bstractWe 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 Nf = 4 massless staggered fermions, we demonstrate that this improvement can remove

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

\mathcal{O}\left( {{a^2}} \right)

Bulk and finite-temperature transitions in SU(3) gauge theories with many light fermions

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

Reaching the chiral limit in many flavor systems

\mathcal{O}\left( {{a^2}} \right)

Finite size scaling and the effect of the gauge coupling in 12 flavor systems

effects. For the finite-volume gradient flow renormalization scheme defined by

Improved Lattice Renormalization Group Techniques

c={{{\sqrt{8t }}} \left/ {L=0.2 } \right.}

MCRG study of 8 and 12 fundamental flavors with mixed fundamental-adjoint gauge action in strong coupling

, we find the continuum conformal fixed point to be located at