# A Method for simulating chiral fermions on the lattice

@article{Kaplan1992AMF, title={A Method for simulating chiral fermions on the lattice}, author={D. Kaplan}, journal={Physics Letters B}, year={1992}, volume={288}, pages={342-347} }

Abstract I show that a lattice theory of massive interacting fermions in 2 n +1 dimensions may be used to simulate the behavior of massless chiral fermions in 2 n dimensions if the fermion mass has a step function shape in the extra dimension. The massless states arise as zero modes bound to the mass defect, and all doublers can be given large gauge invariant masses. The manner in which the anomalies are realized is transparent: apparent chiral anomalies in the 2 n -dimensional subspace… Expand

#### 810 Citations

Chiral Fermions and Anomalies on a Finite Lattice

- Physics
- 1992

Abstract Recently Kaplan proposed a new method to simulate chiral fermions on the lattice by introducing a space dependent mass term that looks like a domain wall. He showed that if one starts with… Expand

Chiral fermions from lattice boundaries

- Physics
- 1993

Abstract We construct a model in which four-dimensional chiral fermions arise on the boundaries of a five-dimensional lattice with free boundary conditions in the fifth direction. The physical… Expand

A Perturbative construction of lattice chiral fermions

- Physics
- 1995

Abstract We perform a renormalization group transformation to construct perturbatively a lattice theory of chiral fermions. The field variables of the continuum theory are averaged over hypercubes to… Expand

Chiral fermions, anomalies and Chern-Simons currents on the lattice

- Physics
- 1993

Abstract I discuss the zeromode spectrum of lattice chiral fermions in the domain wall model suggested recently. In particular I give the critical momenta where the fermions cease to be chiral and… Expand

Anomalies and chiral defect fermions

- Physics
- 1994

Abstract Chiral defect fermions in the background of an external, 2n-dimensional gauge field are considered. Assuming first a finite extra dimension, we calculate the axial anomaly in a vector-like,… Expand

The euclidean spectrum of Kaplan's lattice chiral fermions

- Physics
- 1993

Abstract We consider the (2 n + 1)-dimensional euclidean Dirac operator with a mass term that looks like a domain wall, recently proposed by Kaplan to describe chiral fermions in 2 n dimensions. In… Expand

Chern-Simons currents and chiral fermions on the lattice

- Physics
- 1993

Abstract We compute the Chern-Simons current induced by lattice fermions on a d(=2n+1)-dimensional lattice, using a topological interpretation of the fermion propagator as a map from the torus to the… Expand

Constraints on the existence of chiral fermions in interacting lattice theories.

- Physics, Medicine
- Physical review letters
- 1993

Abstract Any interacting theory defined on a regular lattice is shown to have a vector-like spectrum if the following conditions are satisfied: (a) hermiticity, (b) locality, (c) relativistic… Expand

Chiral fermions on the lattice

- Physics
- 1995

Abstract The overlap approach to chiral gauge theories on arbitrary D-dimensional lattices is studied. The doubling problem and its relation to chiral anomalies for D = 2 and 4 is examined. In each… Expand

Parity-invariant lattice regularization of a three-dimensional gauge-fermion system

- Physics
- 1997

Abstract In three dimensions, the effective action for the gauge field induced by integrating out a massless Dirac fermion is known to give either a parity-invariant or a parity-violating result,… Expand

#### References

SHOWING 1-10 OF 71 REFERENCES

Chiral Fermions and Anomalies on a Finite Lattice

- Physics
- 1992

Abstract Recently Kaplan proposed a new method to simulate chiral fermions on the lattice by introducing a space dependent mass term that looks like a domain wall. He showed that if one starts with… Expand

Chiral Symmetry on the Lattice with Wilson Fermions

- Physics
- 1985

Abstract The chiral properties of the continuum limit of lattice QCD with Wilson fermions are studied. We show that a partially conserved axial current can be defined, satisfying the usual current… Expand

Neutrinos on the lattice. The regularization of a chiral gauge theory

- Physics
- 1989

Abstract We discuss the explicit construction of a regularized, e.g. lattice, chiral gauge theory, with or without elementary Higgs fields. In contrast with the vector-like case of QCD, the… Expand

Chiral lattice fermions with correct vacuum polarization and chiral anomaly.

- Physics, Medicine
- Physical review. D, Particles and fields
- 1991

An action for chiral lattice fermions is proposed, which avoids the Nielsen-Ninomiya theorem by virtue of its nonlocality and nonbilinearity. The action is constructed by eliminating the extra… Expand

Lattice Fermions: Species Doubling, Chiral Invariance, and the Triangle Anomaly

- Physics
- 1981

Abstract We investigate the formulation of fermions in lattice gauge theories, in weak coupling perturbation theory. It is shown that a lattice fermion formulation without species doubling and with… Expand

On lattice definitions of chiral gauge theories and the problem of anomalies

- Physics
- 1991

Abstract We argue that many lattice formulations of chiral gauge theories cannot reproduce the continuum theories that they are supposed to define. The lattice models contain global symmetries that… Expand

Light composite fermions

- Physics
- 1980

Abstract In this paper we consider the possibility that QCD-like theories can lead to massless or near-massless composite fermions. The method of analysis relies on a conjectured equivalence between… Expand

Lattice fermions in euclidean space-time

- Physics
- 1981

Abstract A very short proof of a no-go theorem for putting fermions on a lattice is given using the Poincare-Hopf theorem. The no-go theorem forbids the lattice formulation of theories with handed… Expand

Axionic strings: Covariant anomalies and bosonization of chiral zero modes

- Physics
- 1988

Abstract We show that the chiral zero modes of fermions coupled to an axionic string provide a physical realization of covariant gauge and gravitational anomalies in two dimensions. We develop a… Expand

Perturbative tests of a lattice fermion proposal of Quinn and Weinstein.

- Physics, Medicine
- Physical review. D, Particles and fields
- 1988

It is argued that the construction of such counterterms would entail at least a partial breaking of the chiral symmetry, and in order to obtain a satisfactory continuum limit, one would need to augment the Quinn-Weinstein proposal through the inclusion of additional counterterms. Expand