Noncommutative Chiral Gauge Theories on the Lattice with Manifest Star-Gauge Invariance
arXiv:hep-th/0107110 · doi:10.1088/1126-6708/2001/08/033
Abstract
We show that noncommutative U(r) gauge theories with a chiral fermion in the adjoint representation can be constructed on the lattice with manifest star-gauge invariance in arbitrary even dimensions. Chiral fermions are implemented using a Dirac operator which satisfies the Ginsparg-Wilson relation. A gauge-invariant integration measure for the fermion fields can be given explicitly, which simplifies the construction as compared with lattice chiral gauge theories in ordinary (commutative) space-time. Our construction includes the cases where continuum calculations yield a gauge anomaly. This reveals a certain regularization dependence, which is reminiscent of parity anomaly in commutative space-time with odd dimensions. We speculate that the gauge anomaly obtained in the continuum calculations in the present cases can be cancelled by an appropriate counterterm.
23 pages, 1 figure. LaTeX, epsf. v3: Reference added and typos corrected. Final version published in Journal of High Energy Physics
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