Step scaling and the Yang-Mills gradient flow

Abstract

The use of the Yang-Mills gradient flow in step-scaling studies of lattice QCD is expected to lead to results of unprecedented precision. Step scaling is usually based on the Schrödinger functional, where time ranges over an interval [0,T] and all fields satisfy Dirichlet boundary conditions at time 0 and T. In these calculations, potentially important sources of systematic errors are boundary lattice effects and the infamous topology-freezing problem. The latter is here shown to be absent if Neumann instead of Dirichlet boundary conditions are imposed on the gauge field at time 0. Moreover, the expectation values of gauge-invariant local fields at positive flow time (and of other well localized observables) that reside in the center of the space-time volume are found to be largely insensitive to the boundary lattice effects.

Plain TeX source, 26 pages, 7 figures; v2: corrected typos and updated references

References in corpus (3)

• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Critical slowing down and error analysis in lattice QCD simulations
• Non-renormalizability of the HMC algorithm

Cited by in corpus (8)

• The lattice gradient flow at tree-level and its improvement
• Slow running of the Gradient Flow coupling from 200 MeV to 4 GeV in $N_{\mathrm{f}}=3$ QCD
• Locally smeared operator product expansions in scalar field theory
• The perturbative QCD gradient flow to three loops
• The gradient flow running coupling with twisted boundary conditions
• Generalized Gradient Flow Equation and Its Application to Super Yang-Mills Theory
• Diffusion of topological charge in lattice QCD simulations
• Instantaneous stochastic perturbation theory