Symanzik improvement of the gradient flow in lattice gauge theories
Abstract
We apply the Symanzik improvement programme to the 4+1dimensional local reformulation of the gradient flow in pure SU( N) lattice gauge theories. We show that the classical nature of the flow equation allows one to eliminate all cutoff effects at O(a^2), which originate either from the discretised gradient flow equation or from the gradient flow observable. All the remaining O(a^2) effects can be understood in terms of local counterterms at the zero flowtime boundary. We classify these counterterms and provide a complete set as required for onshell improvement. Compared to the 4dimensional 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 nontrivial order in the coupling.
 Publication:

European Physical Journal C
 Pub Date:
 January 2016
 DOI:
 10.1140/epjc/s1005201538319
 arXiv:
 arXiv:1508.05552
 Bibcode:
 2016EPJC...76...15R
 Keywords:

 High Energy Physics  Lattice
 EPrint:
 37 Pages, 1 useful equation