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

TL;DR

This paper develops a lattice formulation for noncommutative chiral gauge theories with star-gauge invariance, using Ginsparg-Wilson fermions, and discusses anomaly regularization and potential cancellation.

Contribution

It introduces a lattice construction for noncommutative chiral gauge theories with manifest star-gauge invariance, including explicit fermion measure and anomaly analysis.

Findings

Lattice formulation with Ginsparg-Wilson fermions preserves star-gauge invariance.

Explicit fermion measure simplifies chiral gauge theory construction.

Continuum anomalies can be regularized and potentially canceled by counterterms.

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.