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arXiv · hep-th/0107110

Noncommutative Chiral Gauge Theories on the Lattice with Manifest Star-Gauge Invariance

J. Nishimura·M. A. Vazquez-Mozo
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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.

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J. Nishimura, M. A. Vazquez-Mozo. 2001-09-13. Noncommutative Chiral Gauge Theories on the Lattice with Manifest Star-Gauge Invariance. https://doi.org/10.1088/1126-6708%2F2001%2F08%2F033

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