Regularizing QCD with staggered fermions and the fourth root trick

We investigate the properties of staggered-fermion lattice QCD in which the fourth root of the fermion determinant is taken. We show that this theory is non-local at non-zero lattice spacing $a$, and that the non-locality is caused by the breaking of taste symmetry at $a\ne 0$. We then present a renormalization-group based argument that the theory restores taste symmetry in the continuum limit. As a consequence the theory is local in that limit, and falls into the correct universality class. Finally, we argue that the correct effective theory for the physics of Goldstone bosons at $a\ne 0$ is given by staggered chiral perturbation theory with the replica trick.