  The graphene-inspired fermion actions recently proposed by Creutz and Borici
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.
