The Schrodinger functional with chirally rotated boundary conditions

Abstract

Using orbifold techniques I construct the Schrodinger functional (SF) for a doublet of Wilson quarks with chirally rotated boundary conditions. This allows to perform checks of universality: for instance, the renormalized SF coupling constant, defined with either boundary conditions, must have a unique continuum limit. Similarly, SF correlation functions in twisted mass QCD and standard QCD can be defined such that they share a common continuum limit. An additional benefit of the new set-up consists in the observation that all the bulk O(a) counterterms to the action and composite operators become irrelevant in the chiral limit. This implies that (ratios of) SF renormalization constants can be automatically O(a) improved, up to the effect of unavoidable boundary counterterms. As a first application we calculate the running coupling for Nf=2 flavours in the SF-scheme to one-loop order of perturbation theory. Universality of the continuum limit is confirmed and the irrelevance of the Sheikholeslami-Wohlert term in the action is demonstrated explicitly