Effective Field Theory for the Anisotropic Wilson Lattice Action

We construct the effective field theory appropriate for describing the low energy behavior of anisotropic Wilson lattice actions and the O(a) improved variant thereof. We then apply this effective field theory to the hadron spectrum and dispersion relations, focussing on the corrections due to the anisotropy. We point out an important feature of anisotropic lattices regarding the Aoki-regime; for a given set of fermion masses and spatial lattice spacing, if an isotropic action is in the QCD-phase, this does not guarantee that the anisotropic action is outside the Aoki-regime. This may be important in the tuning of bare parameters for anisotropic lattices using domain-wall and overlap fermions as well as Wilson and O(a)-improved Wilson fermions.