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

Nishimura, Jun; Vázquez-Mozo, Miguel Angel

doi:10.1088/1126-6708/2001/08/033

Cited by 44 publications

(56 citation statements)

References 51 publications

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“…Note added: A lattice construction of noncommutative theories with adjoint chiral fermions, for arbitrary even dimensions, was recently reported in [31]. In d = 2 mod 4 dimensions, the adjoint chiral fermion is not vector-like and would contribute to anomalies in the commutative context.…”

Section: Comments On Noncommutative Higgsed Theories Like the Noncommentioning

confidence: 99%

★-Wars episode I: the phantom anomaly

Intriligator

Kumar

2002

Nuclear Physics B

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As pointed out, chiral non-commutative theories exist, and examples can be constructed via string theory. Gauge anomalies require the matter content of individual gauge group factors, including U (1) factors, to be non-chiral. All "bad" mixed gauge anomalies, and also all "good" (e.g. for π 0 → γγ) ABJ type flavor anomalies, automatically vanish in non-commutative gauge theories. We interpret this as being analogous to string theory, and an example of UV/IR mixing: non-commutative gauge theories automatically contain "closed string," Green-Schwarz fields, which cancel these anomalies.

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Section: Comments On Noncommutative Higgsed Theories Like the Noncommentioning

confidence: 99%

★-Wars episode I: the phantom anomaly

Intriligator

Kumar

2002

Nuclear Physics B

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“…The configuration space can be naturally decomposed into topological sectors by the index of the overlap Dirac operator on the discretized NC torus [47,48,50]. Let us define the covariant forward (backward) difference operator 6) where the SU(N ) matrices Γ µ (µ = 1, 2) satisfy the 't Hooft-Weyl algebra…”

Section: Jhep10(2007)024mentioning

confidence: 99%

Probability distribution of the index in gauge theory on 2d non-commutative geometry

Aoki¹,

Nishimura²,

Susaki³

2007

J. High Energy Phys.

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Probability distribution of the index in gauge theory on 2d non-commutative geometryTo cite this article: Hajime Aoki et al JHEP10 (2007)024 View the article online for updates and enhancements. Abstract: We investigate the effects of non-commutative geometry on the topological aspects of gauge theory using a non-perturbative formulation based on the twisted reduced model. The configuration space is decomposed into topological sectors labeled by the index ν of the overlap Dirac operator satisfying the Ginsparg-Wilson relation. We study the probability distribution of ν by Monte Carlo simulation of the U(1) gauge theory on 2d non-commutative space with periodic boundary conditions. In general the distribution is asymmetric under ν → −ν, reflecting the parity violation due to non-commutative geometry. In the continuum and infinite-volume limits, however, the distribution turns out to be dominated by the topologically trivial sector. This conclusion is consistent with the instanton calculus in the continuum theory. However, it is in striking contrast to the known results in the commutative case obtained from lattice simulation, where the distribution is Gaussian in a finite volume, but the width diverges in the infinite-volume limit. We also calculate the average action in each topological sector, and provide deeper understanding of the observed phenomenon. Related content

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“…In the literature it is common to start from a finite-N matrix model, which is then shown to be equivalent to the lattice formulation of a noncommutative field theory. Indeed, the matrix model representation has proven useful for numerical analyses [15,16,18,20]. Here we will work directly with the lattice formulation and derive the Feynman rules, which are used in the perturbative evaluation of the effective action induced by fermions.…”

Section: Lattice Perturbation Theory In Noncommutative Geometrymentioning

confidence: 99%

“…The noncommutative version of the Ginsparg-Wilson fermion can be obtained by simply using the covariant derivatives (2.19) or (2.21) depending on the representation, instead of the usual ones without star-products. In even dimensions Ginsparg-Wilson fermions played a crucial role in introducing chirality on a discretized noncommutative torus [20]. Recently an analogous construction has been worked out on a fuzzy sphere [49].…”

Section: Noncommutative Chern-simons Theory On the Latticementioning

confidence: 99%

“…Although the most important virtue of the lattice regularization lies in its capability of nonperturbative studies, it has also been used to clarify subtle issues in perturbative aspects of gauge theories. We consider this particularly important because the lattice construction of noncommutative chiral gauge theories suggests a new mechanism of gauge anomaly cancellation, which is not yet known in the continuum [20]. As an application of the lattice perturbation theory, we pick up a noncommutative version of three-dimensional QED, where the lattice calculation indeed plays a crucial role in revealing peculiar properties of the parity anomaly, given in terms of noncommutative Chern-Simons action.…”

Section: Introductionmentioning

confidence: 99%

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Lattice perturbation theory in noncommutative geometry and parity anomaly in 3d noncommutative QED

Nishimura

Vázquez-Mozo

2003

J. High Energy 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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Noncommutative chiral gauge theories on the lattice with manifest star-gauge invariance

Cited by 44 publications

References 51 publications

★-Wars episode I: the phantom anomaly

★-Wars episode I: the phantom anomaly

Probability distribution of the index in gauge theory on 2d non-commutative geometry

Lattice perturbation theory in noncommutative geometry and parity anomaly in 3d noncommutative QED

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