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.

11 pages, 9 figures

References in corpus (9)

• High-precision scale setting in lattice QCD
• Infinite N phase transitions in continuum Wilson loop operators
• The lattice gradient flow at tree-level and its improvement
• Lattice simulations with eight flavors of domain wall fermions in SU(3) gauge theory
• Topological susceptibility and the sampling of field space in $N_f=2$ lattice QCD simulations
• Slow running of the Gradient Flow coupling from 200 MeV to 4 GeV in $N_{\mathrm{f}}=3$ QCD
• Nonperturbative beta function of eight-flavor SU(3) gauge theory
• Large scale separation and hadronic resonances from a new strongly interacting sector
• Gradient flow step-scaling function for SU(3) with ten fundamental flavors

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