A modified formulation of the Schrödinger functional (SF) is proposed. In the continuum it is related to the standard SF by a non-singlet chiral field rotation and therefore referred to as the chirally rotated SF ( χSF). On the lattice with Wilson fermions the relation is not exact, suggesting some interesting tests of universality. The main advantage of the χSF consists in its compatibility with the mechanism of automatic O(a) improvement. In this paper the basic set-up is introduced and discussed. Chirally rotated SF boundary conditions are implemented on the lattice using an orbifold construction. The lattice symmetries imply a list of counterterms, which determine how the action and the basic fermionic two-point functions are renormalised and O(a) improved. As with the standard SF, a logarithmically divergent boundary counterterm leads to a multiplicative renormalisation of the quark boundary fields. In addition, a finite dimension 3 boundary counterterm must be tuned in order to preserve the chirally rotated boundary conditions in the interacting theory. Once this is achieved, O(a) effects originating from the bulk action or from insertions of composite operators in the bulk can be avoided by the mechanism of automatic O(a) improvement. The remaining O(a) effects arise from the boundaries and can be cancelled by tuning a couple of O(a) boundary counterterms. The general results are illustrated in the free theory where the Sheikholeslami-Wohlert term is shown to affect correlation functions only at O(a), irrespective of its coefficient.
Nuclear Physics B
- Pub Date:
- June 2011
- High Energy Physics - Lattice
- 51 pages, 2 figures, revised version: improved and extended discussion of Ward identities in section 3 and of the inclusion of counterterms in section 5