The lattice gradient flow at tree-level and its improvement

2014/06/30 by Zoltan Fodor, Zoltán Fodor, Kieran Holland +5 · 6 citations
Engineering · Mathematics · Physics and Astronomy · #Balanced flow #Discretization #Flow (mathematics) #Gauge theory #Geometry #High-Energy Particle Collisions Research #Lattice (music) #Lattice gauge theory #Mathematical analysis #Mathematical physics #Mathematics #Observable #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Square lattice #Square root #Statistical physics #Superconducting Materials and Applications #Tree (set theory) #hep-lat

paper · pdf · doi:10.1007/jhep09(2014)018

14 pages, 8 figures, references added, published version

arxiv created 2014/08/19 · openalex publication_date 2014/09/01 · arxiv updated 2015/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

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.

Citations

• ΔMK and epsilonK in SUSY at the next-to-leading order
• Improving the continuum limit of gradient flow step scaling
• Trivializing maps, the Wilson flow and the HMC algorithm
• Critical slowing down and the gradient flow coupling in the Schrödinger functional
• The gradient flow in a twisted box
• The Gradient Flow Coupling in Minimal Walking Technicolor

Cited by

• Lattice gradient flow with tree-level O(a⁴) improvement in pure Yang-Mills theory
• Numerical study of tree-level improved lattice gradient flows in pure Yang-Mills theory
• Machine-learned RG-improved gauge actions and classically perfect gradient flows
• The twelve-flavor β-function and dilaton tests of the sextet scalar
• Gradient flow of O(N) nonlinear sigma model at large N
• Status of a minimal composite Higgs theory

Related

• Lattice gradient flow with tree-level O(a⁴) improvement in pure Yang-Mills theory
• On O(a²) effects in gradient flow observables
• The lattice gradient flow at tree level
• Gradient flow scale setting with tree-level improvement
• Determination of Reference Scales for Wilson Gauge Action from Yang--Mills Gradient Flow