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.
- Publication:
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Nuclear Physics B
- Pub Date:
- February 1995
- DOI:
- 10.1016/0550-3213(95)00118-C
- arXiv:
- arXiv:hep-lat/9501027
- Bibcode:
- 1995NuPhB.443..386R
- Keywords:
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- High Energy Physics - Lattice;
- High Energy Physics - Theory
- E-Print:
- 40 pages, Latex