Classification and Generalization of Minimal-doubling actions

We propose a method to control the number of species of lattice fermions, which yields new classes of minimally doubled lattice fermions with one exact chiral symmetry and exact locality. We classify all the known minimally doubled fermions into two types based on the locations of the propagator poles in the Brillouin zone. We also study higher-dimensional extension of them and show it tends to be more difficult to realize minimal-doubling in higher dimensions.