  In order to study the running coupling in four-flavour QCD, we review the
set-up of the Schr\"odinger functional (SF) with staggered quarks. Staggered
quarks require lattices which, in the usual counting, have even spatial lattice
extent $L/a$ while the time extent $T/a$ must be odd. Setting $T=L$ is
therefore only possible up to ${\rm O}(a)$, which introduces different cutoff
effects already in the pure gauge theory. We re-define the SF such as to cope
with this situation and determine the corresponding classical background field.
A perturbative calculation yields the coefficient of the pure gauge ${\rm
O}(a)$ boundary counterterm to one-loop order.

High Energy Physics - Lattice