title: Symanzik improvement of the gradient flow in lattice gauge theories.
abstract: We apply the Symanzik improvement programme to the [Formula: see text]-dimensional local re-formulation of the gradient flow in pureSU(N) lattice gauge theories. We show that the classical nature of the flow equation allows one to eliminate all cutoff effects at [Formula: see text], which originate either from the discretised gradient flow equation or from the gradient flow observable. All the remaining [Formula: see text] effects can be understood in terms of local counterterms at the zero flow-time boundary. We classify these counterterms and provide a complete set as required for on-shell improvement. Compared to the 4-dimensional pure gauge theory only a single additional counterterm is required, which corresponds to a modified initial condition for the flow equation. A consistency test in perturbation theory is passed and allows one to determine all counterterm coefficients to lowest non-trivial order in the coupling.
authors.affiliation: PH-TH, CERN, 1211 Geneva 23, Switzerland.
authors.forename: Alberto
authors.initials: A
authors.lastname: Ramos
authors.affiliation: School of Mathematics, Trinity College, Dublin, Dublin 2, Ireland.
authors.forename: Stefan
authors.initials: S
authors.lastname: Sint