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

The SF running coupling with four flavours of staggered quarks