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New fermion discretizations and their applications

We review the recent progress in new lattice fermion formulations. We focus on the following three types which have possibility of improving lattice simulations. (1) Flavored-mass fermions are a generalization of Wilson fermions with species-splitting mass terms. In particular, staggered-Wilson fermions initiated by Adams have possibilities of reducing numerical costs in overlap fermions and the influence of taste-breaking in staggered fermions. (2) Central-branch Wilson fermions, in which additive mass renormalization is forbidden by extra axial symmetry, could enable us to perform Wilson-fermion lattice QCD without fine-tuning. (3) Minimally doubled fermions, which reduce the number of species by species-dependent chemical potential terms, realizes a ultra-local chiral fermion at the price of hypercubic symmetry. These setups reveal unknown aspects of lattice fermions, and we obtain a deeper understanding of lattice field theory.