Noncommutative gauge field theories: a no-go theorem

Chaichian, M.; Prešnajder, P.; Sheikh-Jabbari, M. M.; Tureanu, Anca

doi:10.1016/s0370-2693(01)01478-2

Cited by 120 publications

(170 citation statements)

References 20 publications

(21 reference statements)

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“…Equation (2.18) is the same condition we found for the cancellation of dangerous UV/IR infrared singularities for the three-and four-dimensional noncommutative super-Yang-Mills theories [9,10]. Again, we see that the strong restriction imposed on the choice of the gauge group at the classical level [11] also plays an outstanding role to enforce the absence of singularities in the quantum theory.…”

Section: Finiteness In the Pure Gauge Sectorsupporting

confidence: 67%

“…As we shall prove, similarly to other four-and three-dimensional noncommutative supersymmetric gauge theories [9,10], the cancellation of UV/IR singularities, generated in the nonplanar part of the quantum corrections, demands that the gauge group generators are in the fundamental representation of the U(N) group. We recall that this is the same requirement found for the consistency of noncommutative gauge models at the classical level [11]. Second, we will calculate the finite one-loop quantum corrections to the effective action of the supersymmetric theory (see [12] for a similar calculation in the non-supersymmetric case, as well as [13] for an extensive study of the commutative theory).…”

Section: Introductionmentioning

confidence: 84%

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Supersymmetric non-Abelian non-commutative Chern–Simons theory

et al. 2006

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In this work, we study the three-dimensional non-Abelian noncommutative supersymmetric Chern-Simons model with the U (N ) gauge group. Using a superfield formulation, we prove that, for the pure gauge theory, the Green functions are one-loop finite in any gauge, if the gauge superpotential belongs to the fundamental representation of u(N ); this result also holds when matter in the fundamental representation is included. However, the cancellation of both ultraviolet and ultraviolet/infrared infrared divergences only happens in a special gauge if the coupling of the matter is in the adjoint representation. We also look into the finite one-loop quantum corrections to the effective action: in the pure gauge sector the Maxwell together with its corresponding gauge fixing action are generated; in the matter sector, the Chern-Simons term is generated, inducing a shift in the classical Chern-Simons coefficient. * Electronic address: alysson,mgomes,ajsilva@fma.if.usp.br † Electronic address: petrov@fisica.ufpb.br

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Section: Finiteness In the Pure Gauge Sectorsupporting

confidence: 67%

Section: Introductionmentioning

confidence: 84%

Supersymmetric non-Abelian non-commutative Chern–Simons theory

et al. 2006

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“…In the first approach which is based on the "Seiberg-Witten" maps, the symmetry group, number of gauge fields and particles are the same as the ordinary standard model [47]. Meanwhile, in the second approach the gauge group is U(3) × U(2) × U(1) which can be reduced to the standard model gauge group through appropriate symmetry breaking [48,49]. Here we follow the first approach to do our calculations.…”

Section: Time Evolution Of Stokes Parameters Vs Nc Forward Photon-fementioning

confidence: 99%

Using an intense laser beam in interaction with muon/electron beam to probe the noncommutative QED

Tizchang¹,

Batebi²,

Haghighat³

et al. 2017

J. High Energ. Phys.

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It is known that the linearly polarized photons can partly transform to circularly polarized ones via forward Compton scattering in a background such as the external magnetic field or noncommutative space time. Based on this fact we explore the effects of the NC-background on the scattering of a linearly polarized laser beam from an intense beam of charged leptons. We show that for a muon/electron beam flux ε µ,e ∼ 10 12 /10 10 TeV cm −2 sec −1 and a linearly polarized laser beam with energy k 0 ∼1 eV and average powerP laser 10 3 KW, the generation rate of circularly polarized photons is about R V ∼ 10 4 /sec for noncommutative energy scale Λ NC ∼ 10 TeV. This is fairly large and can grow for more intense beams in near future.

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“…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. Using this method the problems of charge quantization [15,16] and tensor product of gauge groups [14] were solved and the standard model and GUT's were formulated at the tree level on noncommutative space [17,18].…”

Section: Introductionmentioning

confidence: 99%

“…In contrast to earlier approaches [11][12][13][14], this method works for arbitrary gauge groups. Using this method the problems of charge quantization [15,16] and tensor product of gauge groups [14] were solved and the standard model and GUT's were formulated at the tree level on noncommutative space [17,18]. Non(anti)commutative superspaces naturally arise in string theory as well with x − x deformation (canonical deformation) [19], θ − θ deformation [20][21][22] and x−θ deformation [23].…”

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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Noncommutative gauge field theories: a no-go theorem

Cited by 120 publications

References 20 publications

Supersymmetric non-Abelian non-commutative Chern–Simons theory

Supersymmetric non-Abelian non-commutative Chern–Simons theory

Using an intense laser beam in interaction with muon/electron beam to probe the noncommutative QED

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

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