Gauge theory on noncommutative spaces

Field theories on deformed spaces suffer from the IR/UV mixing and renormalization is generically spoiled.In work with R. Wulkenhaar, one of us realized a way to cure this disease by adding one more marginal operator.We review these ideas, show the application to φ 3 models and use the heat kernel expansion methods for a scalar field theory coupled to an external gauge field on a θ-deformed space and derive noncommutative gauge field actions.

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“…finds a remedy to this situation [38]. The gauge field A µ and hence the covariant coordinates transform in the following way:…”

Section: Induced Gauge Theorymentioning

confidence: 99%

Noncommutative QFT and Renormalization

Grosse

Wulkenhaar²

Quantum Gravity

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“…This question is automatically answered by solving the Seiberg-Witten equation in terms of superfields. For this we will apply the method developed by Wess and collaborators in [7][8][9][10] to determine the Seiberg-Witten maps for the superfield case.…”

Section: Construction Of the Seiberg-witten Map In Terms Of Componentmentioning

confidence: 99%

“…This map has become known as the Seiberg-Witten map. In [7][8][9][10] gauge theory on noncommutative space was formulated using the Seiberg-Witten map. In contrast to earlier approaches [11][12][13][14], this method works for arbitrary gauge groups.…”

Section: Introductionmentioning

confidence: 99%

Seiberg-Witten Map for Superfields onN=(1/2,0) andN=(1/2,1/2) Deformed Superspace

Mikulovic¹

2004

J. High Energy Phys.

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In this paper we construct the Seiberg-Witten maps for superfields on the θ − θ deformed superspaces with N = ( 1 2 , 0) and N = ( 1 2 , 1 2 ) supersymmety. We show that on the N = ( 1 2 , 0) deformed superspace there is no SeibergWitten map for antichiral superfields which is at the same time antichiral, local and which preserves the N = ( 1 2 , 0) supersymmetry. Solutions which break this requirements are presented. On the N = ( 1 2 , 1 2 ) deformed superspace we show that for the chiral gauge parameter, and therefore also for the chiral matter field, there is no chiral Seiberg-Witten map. Some other possible Seiberg-Witten maps for the superfields are presented.

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“…finds a remedy to this situation [8]. The gauge field A µ and hence the covariant coordinates transform in the following way:…”

Section: Introductionmentioning

confidence: 99%

Induced gauge theory on a noncommutative space

Wohlgenannt¹

2008

Fortschritte der Physik

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We consider a scalar φ 4 theory on canonically deformed Euclidean space in 4 dimensions with an additional oscillator potential. This model is known to be renormalisable. An exterior gauge field is coupled in a gauge invariant manner to the scalar field. We extract the dynamics for the gauge field from the divergent terms of the 1-loop effective action using a matrix basis and propose an action for the noncommutative gauge theory, which is a candidate for a renormalisable model.

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Gauge theory on noncommutative spaces

Abstract: We introduce a formulation of gauge theory on noncommutative spaces based on the concept of covariant coordinates. Some important examples are discussed in detail. A Seiberg-Witten map is established in all cases.

Cited by 541 publications

References 20 publications

Noncommutative QFT and Renormalization

Noncommutative QFT and Renormalization

Seiberg-Witten Map for Superfields onN=(1/2,0) andN=(1/2,1/2) Deformed Superspace

Induced gauge theory on a noncommutative space

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