Properties and uses of the Wilson flow in lattice QCD

Abstract

Theoretical and numerical studies of the Wilson flow in lattice QCD suggest that the gauge field obtained at flow time t>0 is a smooth renormalized field. The expectation values of local gauge-invariant expressions in this field are thus well-defined physical quantities that probe the theory at length scales on the order of sqrt(t). Moreover, by transforming the QCD functional integral to an integral over the gauge field at a specified flow time, the emergence of the topological (instanton) sectors in the continuum limit becomes transparent and is seen to be caused by a dynamical effect that rapidly separates the sectors when the lattice spacing is reduced from 0.1 fm to smaller values.

Plain TeX source, 21 pages, 4 figures. Corrected figure 2, figure 3 and the quoted values of t0/a^2 in table 1, following the discovery of a bug in the analysis programs (thanks to Yoshifumi Nakamura)

References in corpus (1)

• Chiral symmetry breaking and the Banks--Casher relation in lattice QCD with Wilson quarks

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• Localization of topological charge density near $T_c$ in quenched QCD with Wilson flow
• Large $N$ scaling and factorization in SU($N$) Yang-Mills gauge theory
• Thermal Simulations, Open Boundary Conditions and Switches
• Status of a minimal composite Higgs theory
• Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
• Topological Susceptibility under Gradient Flow
• Dark Walker in the Early Universe: A Strongly Coupled Sector Model
• Stout smearing and Wilson flow in lattice perturbation theory
• Finite temperature QCD with $N_f=2+1+1$ Wilson twisted mass fermions at physical pion, strange and charm masses
• Applications of the Perturbative Gradient Flow
• The electroweak Hamiltonian in the gradient flow formalism
• Topological susceptibility and excess kurtosis in SU(3) Yang-Mills theory
• The determination of potential scales in 2+1 flavor QCD
• Topological data analysis of the deconfinement transition in SU(3) lattice gauge theory
• QCD static force in gradient flow
• Perturbative analysis of the Wess-Zumino flow
• Study of topological quantities of lattice QCD with a modified Wasserstein generative adversarial network
• Phase structure of heavy dense lattice QCD and the three-state Potts model
• Shear and bulk viscosities of the gluon plasma across the transition temperature from lattice QCD
• Topology in the 2d Heisenberg Model under Gradient Flow
• New $N_f=2$ Pseudofermion Action for Monte-Carlo Simulation of Lattice Field Theory with Domain-Wall Fermions
• Precision lattice calculation of the hadronic contribution to the running of the electroweak gauge couplings
• On the chiral anomaly and the Yang-Mills gradient flow
• Lattice investigation of custodial two-Higgs-doublet model at weak quartic couplings
• ${\eta }_c{\eta }_c$ and $J/\psi J/\psi$ scatterings from lattice QCD
• Conserved vector current in QCD-like theories and the gradient flow
• Uniqueness of gauge covariant renormalisation of stochastic 3D Yang-Mills-Higgs
• Construction of lattice Möbius domain wall fermions in the Schrödinger functional scheme
• Conformal window in SU(2) with fundamental fermions
• 4D $\mathcal{N}=1$ SYM supercurrent on the lattice in terms of the gradient flow
• Weakly coupled conformal gauge theories on the lattice
• Taming lattice artifacts with Pauli--Villars fields
• More on the flavor dependence of $m_{\varrho }/f_{\pi }$
• Mass Spectra of $D_s$ and ${\Omega }_c$ in Lattice QCD with $N_f=2+1+1$ Domain-Wall Quarks
• Memory efficient finite volume schemes with twisted boundary conditions
• Gradient-flowed order parameter for spontaneous gauge symmetry breaking
• Accessing the Gluon Momentum Fraction of Nucleons through the Gradient Flow
• Imprints of $U_A(1)$ chiral anomaly and disorder in the Dirac eigenspectrum of QCD at finite temperature
• One-loop matching of the LEFT to the QCD gradient flow
• Rotationally invariant dynamical lattice regulators for Euclidean quantum field theories
• $f_K/f_{\pi }$ in iso-symmetric QCD and the CKM matrix unitarity
• SU(2) gauge theory with one and two adjoint fermions towards the continuum limit
• Scale setting of SU($N$) Yang--Mills theory, topology and large-$N$ volume independence
• Renormalon effect of quasi-PDF in gradient flow formalism
• $\eta$ and ${\eta }^{\prime }$ mesons from $N_f=2+1$ lattice QCD at the physical point using topological charge operators
• Violation of non-Abelian Bianchi identity and QCD topology
• Unpolarized gluon distribution in the nucleon from lattice quantum chromodynamics
• One-loop matching for quark dipole operators in a gradient-flow scheme
• SU(2) gauge theory with $N_f=24$ quarks at non-zero mass
• Topology of the O(3) non-linear sigma model under the gradient flow
• The gradient flow formulation of the electroweak Hamiltonian
• Approaching the Continuum Limit of the Deconfinement Critical Point for $N_{\text{f}}=2$ Staggered Fermions
• Applications of flow models to the generation of correlated lattice QCD ensembles
• Fermions in worldline holography