The gradient flow coupling in the Schrödinger functional

We study the perturbative behavior of the Yang-Mills gradient ow in theSchrodinger Functional, both in the continuum and on the lattice. The energy density ofthe ow eld is used to dene a running coupling at a scale given by the size of the nitevolume box. From our perturbative computation we estimate the size of cuto eects ofthis coupling to leading order in perturbation theory. On a set of Nf = 2 gauge eldensembles in a physical volume of L 0:4 fm we nally demonstrate the suitability of thecoupling for a precise continuum limit due to modest cuto eects and high statisticalprecision