Locality of the fourth root of the staggered-fermion determinant: Renormalization-group approach

Consistency of present day lattice QCD simulations with dynamical ("sea") staggered fermions requires that the determinant of the staggered-fermion Dirac operator, det(D), be equal to det(4)(D-rg)det(T) where D-rg is a local one-flavor lattice Dirac operator, and T is a local operator containing only excitations with masses of the order of the cutoff. Using renormalization-group (RG) block transformations I show that, in the limit of infinitely many RG steps, the required decomposition exists for the free staggered operator in the "flavor representation." The resulting one-flavor Dirac operator D-rg satisfies the Ginsparg-Wilson relation in the massless case. I discuss the generalization of this result to the interacting theory.