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 (19)

• Chiral symmetry and O(a) improvement in lattice QCD
• The Schrödinger Functional - a Renormalizable Probe for Non-Abelian Gauge Theories
• Perturbative analysis of the gradient flow in non-abelian gauge theories
• A Precise Determination of the Running Coupling in the SU(3) Yang-Mills Theory
• Critical slowing down and error analysis in lattice QCD simulations
• On the Schroedinger functional in QCD
• Lattice QCD with open boundary conditions and twisted-mass reweighting
• Lattice QCD without topology barriers
• Chiral symmetry and the Yang--Mills gradient flow
• Theta dependence of SU(N) gauge theories
• Studying the gradient flow coupling in the Schrödinger functional
• The gradient flow coupling in the Schrödinger Functional
• The running coupling from the QCD Schrödinger functional -- a one-loop analysis
• Lattice energy-momentum tensor from the Yang-Mills gradient flow -- inclusion of fermion fields
• Improvement of N_f=3 lattice QCD with Wilson fermions and tree-level improved gauge action
• Space-time symmetries and the Yang-Mills gradient flow
• Computation of the improvement coefficient $c_{\mathrm{sw}}$ to 1-loop with improved gluon actions
• Numerical Stochastic Perturbation Theory for full QCD
• Non-renormalizability of the HMC algorithm

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• FLAG Review 2024
• High precision renormalization of the flavour non-singlet Noether currents in lattice QCD with Wilson quarks
• Slow running of the Gradient Flow coupling from 200 MeV to 4 GeV in $N_{\mathrm{f}}=3$ QCD
• Non-perturbative improvement of the axial current in N_f=3 lattice QCD with Wilson fermions and tree-level improved gauge action
• 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
• SMD-based numerical stochastic perturbation theory
• Short flow-time coefficients of CP-violating operators
• The gradient flow coupling at high-energy and the scale of SU(3) Yang-Mills theory
• Möbius domain-wall fermions on gradient-flowed dynamical HISQ ensembles
• Generalized Gradient Flow Equation and Its Application to Super Yang-Mills Theory
• Lattice determinations of the strong coupling
• Diffusion of topological charge in lattice QCD simulations
• The Yang-Mills gradient flow and SU(3) gauge theory with 12 massless fundamental fermions in a colour-twisted box
• Determination of ${\alpha }_s(m_Z)$ by the non-perturbative decoupling method
• Past, present, and future of precision determinations of the QCD coupling from lattice QCD
• The gradient flow running coupling in SU(2) gauge theory with $N_f=8$ fundamental flavors
• openQ*D code: a versatile tool for QCD+QED simulations
• Instantaneous stochastic perturbation theory
• Gradient flow step-scaling function for SU(3) with $N_f$ = 6 or 4 fundamental flavors
• Determination of the Strong Coupling Constant by the ALPHA Collaboration
• Non-perturbative tests of continuum HQET through small-volume two-flavour QCD
• Stout smearing and Wilson flow in lattice perturbation theory
• Applications of the Perturbative Gradient Flow
• Memory efficient finite volume schemes with twisted boundary conditions