Perfect lattice actions for quarks and gluons Original Research Article

We use perturbation theory to construct perfect lattice actions for quarks and gluons. The renormalized trajectory for free massive quarks is identified by blocking directly from the continuum. We tune a parameter in the renormalization group transformation such that for 1d configurations the perfect action reduces to the nearest-neighbor Wilson fermion action. The fixed point action for free gluons is also obtained by blocking from the continuum. For 2d configurations it reduces to the standard plaquette action. Classically perfect quark and gluon fields, quark-gluon composite operators and vector and axial vector currents are constructed as well. Also the quark-antiquark potential is derived from the classically perfect Polyakov loop. The quark-gluon and three-gluon perfect vertex functions are determined to leading order in the gauge coupling. This work provides a basis for the numerical construction of a lattice action for QCD, which is (approximately) perfect even beyond perturbation theory.