Search for Chiral Fermion Actions on Non-Orthogonal Lattices

The graphene-inspired fermion actions recently proposed by Creutz and Boriçi have sparked interest in the use of non-orthogonal lattices in lattice QCD. These fermion actions have the desired chiral symmetry and have the minimal doubling required by the Nielsen-Ninomiya no-go theorem. However, due to the lack of discrete symmetries, radiative corrections in the gauged lattice theory will lead to the generation of unwanted relevant and marginal operators. Other similarly motivated non-orthogonal fermion actions avoid these unwanted operators, but introduce incorrect continuum behavior or excessive fermion doubling. A delicate balance of symmetry is required for chiral symmetry, minimal doubling, and no relevant operators, and to date, no non-orthogonal lattice action has accomplished this balance.