Parity-invariant lattice regularization of a three-dimensional gauge-fermion system

Narayanan, Rajamani; Nishimura, Jun

doi:10.1016/s0550-3213(97)80017-x

Cited by 27 publications

(28 citation statements)

References 28 publications

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“…See also[51] for an earlier work on the overlap formalism in odd dimensions, where a parity invariant phase choice has been made 5. This gauge violation was also concluded in ref [53],.…”

supporting

confidence: 59%

Relationship between Nitrogen Profile and Reliability of Heavily Oxynitrided Tunnel Oxide Films for Flash Electrically Erasable and Programmable ROMs

Arakawa

Hayashi

Ohno

et al. 1995

Jpn. J. Appl. Phys.

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We formulate lattice perturbation theory for gauge theories in noncommutative geometry. We apply it to three-dimensional noncommutative QED and calculate the effective action induced by Dirac fermions. In particular "parity invariance" of a massless theory receives an anomaly expressed by the noncommutative Chern-Simons action. The coefficient of the anomaly is labelled by an integer depending on the lattice action, which is a noncommutative counterpart of the phenomenon known in the commutative theory. The parity anomaly can also be obtained using Ginsparg-Wilson fermions, where the masslessness is guaranteed at finite lattice spacing. This suggests a natural definition of the lattice-regularized Chern-Simons theory on a noncommutative torus, which could enable nonperturbative studies of quantum Hall systems.

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“…See also[51] for an earlier work on the overlap formalism in odd dimensions, where a parity invariant phase choice has been made 5. This gauge violation was also concluded in ref [53],.…”

supporting

confidence: 59%

Relationship between Nitrogen Profile and Reliability of Heavily Oxynitrided Tunnel Oxide Films for Flash Electrically Erasable and Programmable ROMs

Arakawa

Hayashi

Ohno

et al. 1995

Jpn. J. Appl. Phys.

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“…When applied to Dirac fermions in even dimensions, an exact chiral symmetry is preserved and one can even derive a Dirac operator [11], which gives an explicit solution [12] to the Ginsparg-Wilson relation [13]. When applied to Dirac fermions in odd dimensions, parity invariance can be manifestly preserved [14], and a global gauge anomaly can be correctly reproduced [15]. These symmetries enable a lattice construction of supersymmetric gauge theories without fine-tuning [1,16].…”

Section: Introductionmentioning

confidence: 98%

Translational anomaly in chiral gauge theories on a torus and the overlap formalism

Izubuchi

Nishimura

1999

J. High Energy Phys.

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We point out that a fermion determinant of a chiral gauge theory on a 2D torus has a phase ambiguity proportional to the Polyakov loops along the boundaries, which can be reproduced by the overlap formalism. We show that the requirement on the fermion determinant that a singularity in the gauge field can be absorbed by a change of the boundary condition for the fermions, is not compatible with translational invariance in general. As a consequence, the gauge anomaly for singular gauge transformations discovered by Narayanan-Neuberger actually exists in any 2D U(1) chiral gauge theory unless the theory is vector-like. We argue that the gauge anomaly is peculiar to the overlap formalism with the Wigner-Brillouin phase choice and that it is not necessarily a property required in the continuum. We also generalize our results to any even

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“…This is quite reminiscent of the situation in commutative space-time with odd dimensions. There the parity anomaly conflicts with the gauge symmetry in some cases [25]. If one imposes the gauge invariance, one obtains the parity anomaly.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…Comparing these results with our lattice construction, we observe a certain regularization dependence, which is reminiscent of the parity anomaly in commutative space-time with an odd number of dimensions (See Refs. [25] and references therein). We speculate that the gauge anomaly obtained in the continuum calculations might be cancelled by an appropriate counterterm in these cases.…”

Section: Introductionmentioning

confidence: 99%

Noncommutative chiral gauge theories on the lattice with manifest star-gauge invariance

Nishimura¹,

Vázquez-Mozo²

2001

J. High Energy Phys.

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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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Parity-invariant lattice regularization of a three-dimensional gauge-fermion system

Cited by 27 publications

References 28 publications

Relationship between Nitrogen Profile and Reliability of Heavily Oxynitrided Tunnel Oxide Films for Flash Electrically Erasable and Programmable ROMs

Relationship between Nitrogen Profile and Reliability of Heavily Oxynitrided Tunnel Oxide Films for Flash Electrically Erasable and Programmable ROMs

Translational anomaly in chiral gauge theories on a torus and the overlap formalism

Noncommutative chiral gauge theories on the lattice with manifest star-gauge invariance

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