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.

10 pages, latex, espcrc2.sty

Cited by in corpus (26)

• Quenched Lattice QCD with Domain Wall Fermions and the Chiral Limit
• A new approach to Ginsparg-Wilson fermions
• Approximate Ginsparg-Wilson fermions: A first test
• Testing the fixed-point QCD action and the construction of chiral currents
• Low-Dimensional Long-Range Topological Charge Structure in the QCD Vacuum
• A variant approach to the overlap action
• Super Yang-Mills on the lattice with domain wall fermions
• Low-lying fermion modes, topology and light hadrons in quenched QCD
• Chiral Symmetry, Quark Mass, and Scaling of the Overlap Fermions
• Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality
• Chiral Logs in Quenched QCD
• Domain Wall Fermions with Exact Chiral Symmetry
• Chiral Properties of Pseudoscalar Mesons on a Quenched $20^4$ Lattice with Overlap Fermions
• Domain wall fermions and applications
• Lattice 2001: Reflections
• N* Mass Spectrum from an Anisotropic Action
• Quenched Results for Light Quark Physics with Overlap Fermions
• Progress using generalized lattice Dirac operators to parametrize the Fixed-Point QCD action
• On Witten's global anomaly for higher SU(2) representations
• Nonperturbative renormalization of composite operators with overlap fermions
• Solving the local cohomology problem in U(1) chiral gauge theories within a finite lattice
• A simple construction of fermion measure term in U(1) chiral lattice gauge theories with exact gauge invariance
• Perturbative renormalization of the first two moments of non-singlet quark distributions with overlap fermions
• A construction of the Glashow-Weinberg-Salam model on the lattice with exact gauge invariance
• A numerical solution to the local cohomology problem in U(1) chiral gauge theories
• The staggered domain wall fermion method