Background field method in the gradient flow

Abstract

In perturbative consideration of the Yang--Mills gradient flow, it is useful to introduce a gauge non-covariant term ("gauge-fixing term") to the flow equation that gives rise to a Gaussian damping factor also for gauge degrees of freedom. In the present paper, we consider a modified form of the gauge-fixing term that manifestly preserves covariance under the background gauge transformation. It is shown that our gauge-fixing term does not affect gauge-invariant quantities as the conventional gauge-fixing term. The formulation thus allows a background gauge covariant perturbative expansion of the flow equation that provides, in particular, a very efficient computational method of expansion coefficients in the small flow time expansion. The formulation can be generalized to systems containing fermions.

19 pages, the final version to appear in PTEP

References in corpus (24)

• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions
• The electric dipole moment of the neutron from 2+1 flavor lattice QCD
• Non-Gaussianities in the topological charge distribution of the SU(3) Yang--Mills theory
• The infrared regime of SU(2) with one adjoint Dirac flavour
• Topological susceptibility and the sampling of field space in $N_f=2$ lattice QCD simulations
• Locally smeared operator product expansions in scalar field theory
• Critical endpoint of finite temperature phase transition for three flavor QCD
• On the effects of heavy sea quarks at low energies
• Renormalizability of the gradient flow in the 2D $O(N)$ non-linear sigma model
• Gradient Flow of O(N) nonlinear sigma model at large N
• Generalized Gradient Flow Equation and Its Application to Super Yang-Mills Theory
• Diffusion of topological charge in lattice QCD simulations
• Correlation and localization properties of topological charge density and the pseudoscalar glueball mass in SU(3) lattice Yang-Mills theory
• Determination of Reference Scales for Wilson Gauge Action from Yang--Mills Gradient Flow
• Universal formula for the flavor non-singlet axial-vector current from the gradient flow
• The Yang-Mills gradient flow and renormalization
• Large-$N$ limit of the gradient flow in the 2D $O(N)$ nonlinear sigma model
• A novel approach to the study of conformality in the SU(3) theory with multiple flavors
• Universal formula for the energy--momentum tensor via a flow equation in the Gross--Neveu model
• The running coupling of the minimal sextet composite Higgs model
• The $SU(\infty )$ twisted gradient flow running coupling
• The gradient flow of the Dirac spectrum
• A comparison of updating algorithms for large N reduced models

Cited by in corpus (13)

• Thermodynamics in quenched QCD: energy--momentum tensor with two-loop order coefficients in the gradient flow formalism
• Small flow-time representation of fermion bilinear operators
• Four quark operators for kaon bag parameter with gradient flow
• Proof of the renormalizability of the gradient flow
• 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
• Using Wilson flow to study the SU(3) deconfinement transition
• 4D $\mathcal{N}=1$ SYM supercurrent in terms of the gradient flow
• One-loop matching of $CP$-odd four-quark operators to the gradient-flow scheme
• Energy--momentum tensor on the lattice: recent developments
• Gradient flow representation of the four-dimensional $\mathcal{N}=2$ super Yang--Mills supercurrent
• Axial $U(1)$ anomaly in a gravitational field via the gradient flow
• 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
• One-loop matching of the LEFT to the QCD gradient flow