Chiral Fermions on the Lattice

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 case it is shown that the doublers can be eliminated and the well known perturbative results for chiral anomalies can be recovered. We also consider the multi--flavour case and give the general criteria for the construction of anomaly free chiral gauge theories on arbitrary lattices. We calculate the second order terms in a continuum approximation to the overlap formula in $D$ dimensions and show that they coincide with the bilinear part of the effective action of $D$--dimensional Weyl fermions coupled to a background gauge field. Finally, using the same formalism we reproduce the correct Lorentz, diffeomorphism and gauge anomalies in the coupling of a Weyl fermion to 2--dimensional gravitational and Maxwell fields.

40 pages, Latex

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• Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality
• Consistent and covriant anomalies in the overlap formulation of chiral gauge theories
• On the Overlap Prescription for Lattice Regularization of Chiral Fermions
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• Lattice Chiral Fermions
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• Dirac Fermions and Domain Wall Defects in 2+1 Dimensions
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• Global obstructions to gauge-invariance in chiral gauge theory on the lattice
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• Chiral measurements with the Fixed-Point Dirac operator and construction of chiral currents
• Vacuum Polarization and Chiral Lattice Fermions
• A Lattice Formulation of Chiral Gauge Theories
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• Progress using generalized lattice Dirac operators to parametrize the Fixed-Point QCD action
• Chiral anomalies in the reduced model
• Warped Domain Wall Fermions
• Domain wall fermion and CP symmetry breaking
• Chiral gauge theories on the lattice with exact gauge invariance
• Translational Anomaly in Chiral Gauge Theories on a Torus and the Overlap Formalism
• Majorana and Majorana-Weyl fermions in lattice gauge theory
• Renormalizability of a lattice chiral fermion in the overlap formulation
• Weak coupling expansion of a chiral gauge theory on a lattice in the overlap formulation
• Anomalous gauge theories revisited
• Temperature in Fermion Systems and the Chiral Fermion Determinant
• Domain-wall fermions with $U(1)$ dynamical gauge fields
• Lattice perturbation theory in the overlap formulation for the Yukawa and gauge interactions
• Abelian and non-Abelian Berry curvatures in lattice QCD
• New Regularization Using Domain Wall
• Simple ansatz for the lattice fermion determinant
• Axial anomaly in the reduced model: Higher representations
• Progress in lattice chiral gauge theories
• Wess-Zumino-Witten term on the lattice
• Chiral zero modes on the domain-wall model in 4+1 dimensions
• Domain walls and dimensional reduction
• Chiral symmetry on the lattice
• Regularized overlap and the chiral determinant
• Manifestly Gauge Covariant Treatment of Lattice Chiral Fermions. II
• Tunneling between fermionic vacua and the overlap formalism
• Four-dimensional lattice chiral gauge theories with anomalous fermion content
• Gribov Copy and Complex Phase of Chiral Determinant