Dislocations under gradient flow and their effect on the renormalized coupling

Abstract

Non-zero topological charge is prohibited in the chiral limit of gauge-fermion systems because any instanton would create a zero mode of the Dirac operator. On the lattice, however, the geometric $Q_{\text{geom}}=⟨F\tilde{F}⟩/32{\pi }^2$ definition of the topological charge does not necessarily vanish even when the gauge fields are smoothed for example with gradient flow. Small vacuum fluctuations (dislocations) not seen by the fermions may be promoted to instanton-like objects by the gradient flow. We demonstrate that these artifacts of the flow cause the gradient flow renormalized gauge coupling to increase and run faster. In step-scaling studies such artifacts contribute a term which increases with volume. The usual $a/L\to 0$ continuum limit extrapolations can hence lead to incorrect results. In this paper we investigate these topological lattice artifacts in the SU(3) 10-flavor system with domain wall fermions and the 8-flavor system with staggered fermions. Both systems exhibit nonzero topological charge at the strong coupling, especially when using Symanzik gradient flow. We demonstrate how this artifact impacts the determination of the renormalized gauge coupling and the step-scaling $\beta$ function.

arXiv comment11 pages, 9 figures

References in corpus (45)

• Instantons in QCD
• Properties and uses of the Wilson flow in lattice QCD
• Chiral Fermions from Lattice Boundaries
• Flavor Symmetry and the Static Potential with Hypercubic Blocking
• Analytic Smearing of SU(3) Link Variables in Lattice QCD
• Axial symmetries in lattice QCD with Kaplan fermions
• The index theorem in QCD with a finite cut-off
• High-precision scale setting in lattice QCD
• Trivializing maps, the Wilson flow and the HMC algorithm
• Infinite N phase transitions in continuum Wilson loop operators
• Monte Carlo errors with less errors
• Hypercubic Smeared Links for Dynamical Fermions
• Topological susceptibility in the SU(3) gauge theory
• Strongly interacting dynamics and the search for new physics at the LHC
• Can the nearly conformal sextet gauge model hide the Higgs impostor?
• Nonperturbative investigations of SU(3) gauge theory with eight dynamical flavors
• Instantons from over-improved cooling
• The lattice gradient flow at tree-level and its improvement
• Comparison of the gradient flow with cooling in $SU(3)$ pure gauge theory
• Symanzik improvement of the gradient flow in lattice gauge theories
• Light flavor-singlet scalars and walking signals in $N_f=8$ QCD on the lattice
• Lattice simulations with eight flavors of domain wall fermions in SU(3) gauge theory
• Precision study of the SU(3) topological susceptibility in the continuum
• Improving the Chiral Properties of Lattice Fermions
• Walking signals in Nf=8 QCD on the lattice
• Hadrons and Nuclei
• Low-lying fermion modes, topology and light hadrons in quenched QCD
• Instanton Content of the SU(3) Vacuum
• Nonperturbative beta function of twelve-flavor SU(3) gauge theory
• Slow running of the Gradient Flow coupling from 200 MeV to 4 GeV in $N_{\mathrm{f}}=3$ QCD
• Topological susceptibility and the sampling of field space in $N_f=2$ lattice QCD simulations
• Topological charge using cooling and the gradient flow
• Composite Higgs model at a conformal fixed point
• Nonperturbative beta function of eight-flavor SU(3) gauge theory
• Extended investigation of the twelve-flavor $\beta$-function
• Large scale separation and resonances within LHC range from a prototype BSM model
• Large scale separation and hadronic resonances from a new strongly interacting sector
• Topological susceptibility with the improved Asqtad action
• Gradient flow step-scaling function for SU(3) with twelve flavors
• Continuous renormalization group $\beta$ function from lattice simulations
• Lattice Gauge Theory for Physics Beyond the Standard Model
• Gradient flow step-scaling function for SU(3) with ten fundamental flavors
• Electroweak interactions and dark baryons in the sextet BSM model with a composite Higgs particle
• Topological susceptibility of QCD with dynamical Möbius domain wall fermions
• A new method for the beta function in the chiral symmetry broken phase

Cited by in corpus (5)

• Infrared fixed point and anomalous dimensions in a composite Higgs model
• $\Lambda$ parameter of the SU(3) Yang-Mills theory from the continuous $\beta$ function
• Gradient flow step-scaling function for SU(3) with $N_f=8$ fundamental flavors
• Gradient flow step-scaling function for SU(3) with $N_f$ = 6 or 4 fundamental flavors
• Nonminimal gradient flows in QCD-like theories