The lattice gradient flow at tree-level and its improvement

Abstract

The Yang-Mills gradient flow and the observable E(t), defined by the square of the field strength tensor at t>0, are calculated at finite lattice spacing and tree-level in the gauge coupling. Improvement of the flow, the gauge action and the observable are all considered. The results are relevant for two purposes. First, the discretization of the flow, gauge action and observable can be chosen in such a way that $O(a^2)$, $O(a^4)$ or even $O(a^6)$ improvement is achieved. Second, simulation results using arbitrary discretizations can be tree-level improved by the perturbatively calculated correction factor normalized to one in the continuum limit.

14 pages, 8 figures, references added, published version

References in corpus (5)

• Perturbative analysis of the gradient flow in non-abelian gauge theories
• High-precision scale setting in lattice QCD
• Improving the continuum limit of gradient flow step scaling
• Step scaling and the Yang-Mills gradient flow
• The gradient flow running coupling scheme

Cited by in corpus (15)

• Equation of State for SU(3) Gauge Theory via the Energy-Momentum Tensor under Gradient Flow
• The infrared regime of SU(2) with one adjoint Dirac flavour
• Nonperturbative beta function of eight-flavor SU(3) gauge theory
• Locally smeared operator product expansions in scalar field theory
• The gradient flow running coupling with twisted boundary conditions
• Gradient Flow of O(N) nonlinear sigma model at large N
• The Yang-Mills gradient flow and renormalization
• Numerical study of tree-level improved lattice gradient flows in pure Yang-Mills theory
• Toward the minimal realization of a light composite Higgs
• Energy--momentum tensor on the lattice: recent developments
• Measurement of thermodynamics using gradient flow
• The lattice gradient flow at tree level
• The $SU(\infty )$ twisted gradient flow running coupling
• The gradient flow of the Dirac spectrum
• Gradient Flow Analysis on MILC HISQ Ensembles