Consistent Interactions of the 2+1 Dimensional Noncommutative Chern-Simons Field

Abstract

We consider 2+1 dimensional noncommutative models of scalar and fermionic fields coupled to the Chern-Simons field. We show that, at least up to one loop, the model containing only a fermionic field in the fundamental representation minimally coupled to the Chern-Simons field is consistent in the sense that there are no nonintegrable infrared divergences. By contrast, dangerous infrared divergences occur if the fermion field belongs to the adjoint representation or if the coupling of scalar matter is considered instead. The superfield formulation of the supersymmetric Chern-Simons model is also analyzed and shown to be free of nonintegrable infrared singularities and actually finite if the matter field belongs to the fundamental representation of the supergauge group. In the case of the adjoint representation this only happens in a particular gauge.

minor corrections and some references added

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Cited by in corpus (9)

• Perturbative finiteness of the three-dimensional Susy QED to all orders
• Supersymmetric non-Abelian noncommutative Chern-Simons theory
• On duality of the noncommutative Maxwell-Chern-Simons theory
• A Vector Supersymmetry in Noncommutative U(1) Gauge Theory with the Slavnov Term
• Induced Chern-Simons action on noncommutative torus
• Non-Commutative (Softly Broken) Supersymmetric Yang-Mills-Chern-Simons
• Three-dimensional noncommutative Yukawa theory: Induced effective action and propagating modes
• Perturbative aspects of mass-deformed N=3 Chern-Simons-matter theory
• About the self-dual Chern-Simons system and Toda field theories on the noncommutative plane