Search for Fermion Actions on Hyperdiamond Lattices

Understand

Fermions moving in a two-dimensional honeycomb lattice (graphene) have, at low energies, chiral symmetry.

• Generalizing this construction to four dimensions potentially provides fermions with chiral symmetry and only the minimal fermion doubling demanded by the Nielsen-Ninomiya no-go theorem.
• The practical usefulness of such fermions hinges on whether the action has a necessary set of discrete symmetries of the lattice.
• If this is the case, one avoids the generation of dimension three and four operators which require fine tuning.