Chiral fermions on the lattice

Abstract

Chiral fermions resisted being put on the lattice for twenty years. This raised the suspicion that asymptotically free chiral gauge theories were not renormalizable outside perturbation theory and therefore could not be mathematically extended to infinite energies. During the last several years the situation has reversed itself. Today we believe that all the essential ingredients for a full lattice definition of non-anomalous chiral gauge theories are in place within the overlap construction. This construction is based on earlier work by Callan and Harvey, by Kaplan and by Frolov and Slavnov. It can be reinterpreted as coming from the Ginsparg-Wilson relation, but, at the moment, it is a unique construction and therefore might also be the way by which Nature itself regularizes chiral fermions. This is yet another instance in which lattice field theory makes a potentially important contribution to fundamental particle physics.