Perturbative analysis of the gradient flow in non-abelian gauge theories

Abstract

The gradient flow in non-abelian gauge theories on R^4 is defined by a local diffusion equation that evolves the gauge field as a function of the flow time in a gauge-covariant manner. Similarly to the case of the Langevin equation, the correlation functions of the time-dependent field can be expanded in perturbation theory, the Feynman rules being those of a renormalizable field theory on R^4 x [0,oo). For any matter multiplet and to all loop orders, we show that the correlation functions are finite, i.e. do not require additional renormalization, once the theory in four dimensions is renormalized in the usual way. The flow thus maps the gauge field to a one-parameter family of smooth renormalized fields.

Plain TeX source, 28 pages, 14 figures; v2: typos corrected, agrees with published version

Cited by in corpus (130)

• FLAG Review 2021
• High-precision scale setting in lattice QCD
• Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions
• Critical slowing down and error analysis in lattice QCD simulations
• The strong coupling from a nonperturbative determination of the $\Lambda$ parameter in three-flavor QCD
• The lattice gradient flow at tree-level and its improvement
• Equation of State for SU(3) Gauge Theory via the Energy-Momentum Tensor under Gradient Flow
• SU(N) gauge theories in 3+1 dimensions: glueball spectrum, string tensions and topology
• FLAG Review 2024
• Opportunities for Fundamental Physics Research with Radioactive Molecules
• Heavy quark momentum diffusion from the lattice using gradient flow
• Slow running of the Gradient Flow coupling from 200 MeV to 4 GeV in $N_{\mathrm{f}}=3$ QCD
• Fate of the conformal fixed point with twelve massless fermions and SU(3) gauge group
• Quark Mass Dependence of Heavy Quark Diffusion Coefficient from Lattice QCD
• Locally smeared operator product expansions in scalar field theory
• The perturbative QCD gradient flow to three loops
• Step scaling and the Yang-Mills gradient flow
• Anisotropic pressure induced by finite-size effects in SU(3) Yang-Mills theory
• Topology and axions in QCD
• Strong dynamics, composite Higgs and the conformal window
• $F_K/F_{\pi }$ from Möbius domain-wall fermions solved on gradient-flowed HISQ ensembles
• Ratio of kaon and pion leptonic decay constants with $N_f=2+1+1$ Wilson-clover twisted-mass fermions
• Correlations of Energy-Momentum Tensor via Gradient Flow in SU(3) Yang-Mills Theory at Finite Temperature
• Towards the determination of the gluon helicity distribution in the nucleon from lattice quantum chromodynamics
• Glueballs and Strings in $Sp(2N)$ Yang-Mills theories
• The Yang-Mills gradient flow in finite volume
• The sphaleron rate from Euclidean lattice correlators: an exploration
• Heavy quark diffusion coefficient with gradient flow
• The gradient flow running coupling with twisted boundary conditions
• Classical and Quantum Computing of Shear Viscosity for $2+1D$ SU(2) Gauge Theory
• Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics
• Renormalizability of the gradient flow in the 2D $O(N)$ non-linear sigma model
• Topological susceptibility of pure gauge theory using Density of States
• Short flow-time coefficients of CP-violating operators
• Four quark operators for kaon bag parameter with gradient flow
• Scale setting the Möbius Domain Wall Fermion on gradient-flowed HISQ action using the omega baryon mass and the gradient-flow scales $t_0$ and $w_0$
• Power corrections from decoupling of the charm quark
• Generalized Gradient Flow Equation and Its Application to Super Yang-Mills Theory
• Viscosity of pure-glue QCD from the lattice
• Lattice determinations of the strong coupling
• Correlation and localization properties of topological charge density and the pseudoscalar glueball mass in SU(3) lattice Yang-Mills theory
• The gradient flow running coupling scheme
• Latent heat and pressure gap at the first-order deconfining phase transition of SU(3) Yang-Mills theory using the small flow-time expansion method
• Determination of ${\alpha }_s(m_Z)$ by the non-perturbative decoupling method
• Color Screening in Quantum Chromodynamics
• Moments of parton distribution functions of any order from lattice QCD
• Past, present, and future of precision determinations of the QCD coupling from lattice QCD
• Mass sum rule of hadrons in the QCD instanton vacuum
• Sparse modeling approach to obtaining the shear viscosity from smeared correlation functions
• Distribution of Energy-Momentum Tensor around a Static Quark in the Deconfined Phase of SU(3) Yang-Mills Theory
• Dyon structures in the deconfinement phase of lattice gluodynamics: topological clusters, holonomies and Abelian monopoles
• Effective electroweak Hamiltonian in the gradient-flow formalism
• Gradient flow exact renormalization group
• Three-body forces and Efimov physics in nuclei and atoms
• On O($a^2$) effects in gradient flow observables
• Anisotropy tuning with the Wilson flow
• Spectral and transport properties from lattice QCD
• Topology of $SU(N)$ lattice gauge theories coupled with ${\mathbb{Z}}_N$ $2$-form gauge fields
• The Yang-Mills gradient flow and renormalization
• Glue in hadrons at medium resolution and the QCD instanton vacuum
• QCD Static Force in Gradient Flow
• The twisted gradient flow coupling at one loop
• One-loop matching of $CP$-odd four-quark operators to the gradient-flow scheme
• Gradient flow exact renormalization group -- inclusion of fermion fields
• Numerical study of tree-level improved lattice gradient flows in pure Yang-Mills theory
• Fixed Point Structure of Gradient Flow Exact Renormalization Group for Scalar Field Theories
• On the equivalence between the Wilson flow and stout-link smearing
• Energy--momentum tensor on the lattice: recent developments
• Lattice $B$-field correlators for heavy quarks
• Status and challenges of simulations with dynamical fermions
• Chiral anomaly as a composite operator in the gradient flow exact renormalization group formalism
• Measurement of thermodynamics using gradient flow
• Temperature Dependence of Heavy Quark Diffusion from (2+1)-flavor Lattice QCD
• The lattice gradient flow at tree level
• Comparison of different lattice definitions of the topological charge
• Short-flow-time expansion of quark bilinears through next-to-next-to-leading order QCD
• Off-lightcone Wilson-line operators in gradient flow
• Lattice simulations of adjoint QCD with one Dirac overlap fermion
• The running coupling of 8 flavors and 3 colors
• Heavy Wilson Quarks and O($a$) Improvement: Nonperturbative Results for $b_{\mathrm{g}}$
• Renormalization of the energy-momentum tensor in three-dimensional scalar $SU(N)$ theories using the Wilson flow
• The $SU(\infty )$ twisted gradient flow running coupling
• Machine-learned RG-improved gauge actions and classically perfect gradient flows
• Static force from generalized Wilson loops on the lattice using the gradient flow
• Relative scale setting for two-color QCD with Nf=2 Wilson fermions
• Lattice energy-momentum tensor from the Yang-Mills gradient flow -- a simpler prescription
• The gradient flow running coupling in SU2 with 8 flavors
• Encoding field theories into gravities
• Precision Determination of ${\alpha }_s$ from Lattice QCD
• Schrödinger functional boundary conditions and improvement for N>3
• Gradient Flow: Perturbative and Non-Perturbative Renormalization
• ftint: Calculating gradient-flow integrals with pySecDec
• Equation of state in (2+1)-flavor QCD at physical point with improved Wilson fermion action using gradient flow
• Supersymmetric gradient flow in 4d N=1 SQCD
• The gradient flow of the Dirac spectrum
• Two-loop gradient-flow renormalization of scalar QCD
• Latent heat and pressure gap at the first-order deconfining phase transition of SU(3) Yang-Mills theory using the small flow-time expansion method
• Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
• A basis of the gradient flow exact renormalization group for gauge theory
• Numerical determination of the $\Lambda$-parameter in SU(3) gauge theory from the twisted gradient flow coupling
• Stout smearing and Wilson flow in lattice perturbation theory
• Nonminimal gradient flows in QCD-like theories
• Perturbative analysis of the Wess-Zumino flow
• Topological susceptibility and excess kurtosis in SU(3) Yang-Mills theory
• Lattice investigation of custodial two-Higgs-doublet model at weak quartic couplings
• The electroweak Hamiltonian in the gradient flow formalism
• Shear and bulk viscosities of the gluon plasma across the transition temperature from lattice QCD
• QCD static force in gradient flow
• Euclidean correlation functions of the topological charge density
• On the chiral anomaly and the Yang-Mills gradient flow
• A state space for 3D Euclidean Yang-Mills theories
• $t\to 0$ extrapolation function in SF$t$X method for the energy-momentum tensor
• Conserved vector current in QCD-like theories and the gradient flow
• Applications of the Perturbative Gradient Flow
• Manifestly gauge invariant exact renormalization group for quantum electrodynamics
• Gradient-flowed order parameter for spontaneous gauge symmetry breaking
• Accessing the Gluon Momentum Fraction of Nucleons through the Gradient Flow
• One-loop matching of the LEFT to the QCD gradient flow
• 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
• Study of thermal SU(3) supersymmetric Yang-Mills theory and near-conformal theories from the gradient flow
• Classifying topological sector via machine learning
• Perturbative O($a^2$) effects in gradient flow couplings with SF and SF-open boundary conditions
• The gradient flow formulation of the electroweak Hamiltonian
• Single static-quark system above $T_c$ investigated by energy-momentum tensor in SU(3) Yang-Mills theory
• One-loop matching for quark dipole operators in a gradient-flow scheme
• Unpolarized gluon distribution in the nucleon from lattice quantum chromodynamics
• Non-perturbative improvement and renormalization of the axial current in N_f=3 lattice QCD
• Memory efficient finite volume schemes with twisted boundary conditions