Chiral Lattice Theories From Staggered Fermions

We construct lattice theories from reduced staggered fermions in four dimensions that we argue are capable of producing chiral theories in the continuum limit. The construction employs Yukawa interactions of Fidkowski-Kitaev type which depend on the lattice site parity. We propose that such interactions are capable of generating cut-off scale masses for half of the lattice fermions while preserving all symmetries. We argue that the remaining lattice fermions organize themselves in the continuum limit into a set of sixteen massless Majorana or equivalently Weyl fermions. We show in the context of the lattice model how this fermion content is needed to cancel off a discrete anomaly arising in the continuum limit.