On the equivalence between the Wilson flow and stout-link smearing

Abstract

We present the numerical equivalence between the Wilson flow and stout-link smearing, both of which are known to be a relatively new technique for smoothing the gauge fields on the lattice. Although the conceptional correspondence between two methods was first pointed out by Lüscher in his original paper [J. High Energy Phys.~08 (2010) 071], we provide a direct analytical proof of the equivalence between the two methods at finite lattice spacing $a$ in the zero limit of the stout-smearing parameter $\rho$. The leading order corrections start at $\mathcal{O}(\rho )$, which would induce $\mathcal{O}(a^2)$ corrections. It is, therefore, not obvious that they remain equivalent even with finite parameters ($a\ne 0$ and $\rho \ne 0$) within some numerical precision. In this paper, we demonstrate the equivalence of both methods by directly comparing the expectation value of the action density, which is measured in actual numerical simulations.

22 pages, 7 figures; v2: major updates regarding to analytic proof of the equivalence of two methods, conclusions remain unchanged, v3: version published in PRD

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• Perturbative analysis of the gradient flow in non-abelian gauge theories
• 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
• The perturbative QCD gradient flow to three loops
• The gradient flow running coupling with twisted boundary conditions
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Cited by in corpus (4)

• Numerical evidence for fractional topological objects in SU(3) gauge theory
• Stout smearing and Wilson flow in lattice perturbation theory
• Topological susceptibility and excess kurtosis in SU(3) Yang-Mills theory
• Renormalon effect of quasi-PDF in gradient flow formalism