The coupling of fermions to the three-dimensional noncommutative $C{P}^{N-1}$ model: minimal and supersymmetric extensions

Abstract

We consider the coupling of fermions to the three-dimensional noncommutative $C{P}^{N-1}$ model. In the case of minimal coupling, although the infrared behavior of the gauge sector is improved, there are dangerous (quadratic) infrared divergences in the corrections to the two point vertex function of the scalar field. However, using superfield techniques we prove that the supersymmetric version of this model with ``antisymmetrized'' coupling of the Lagrange multiplier field is renormalizable up to the first order in $\frac{1}{N}$. The auxiliary spinor gauge field acquires a nontrivial (nonlocal) dynamics with a generation of Maxwell and Chern-Simons noncommutative terms in the effective action. Up to the 1/N order all divergences are only logarithimic so that the model is free from nonintegrable infrared singularities.

Minor corrections in the text and modifications in the list of references

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Cited by in corpus (11)

• On the finiteness of noncommutative supersymmetric QED${}_3$ in the covariant superfield formulation
• The three-dimensional non-anticommutative superspace
• On the consistency of the three-dimensional noncommutative supersymmetric Yang-Mills theory
• On the finiteness of the noncommutative supersymmetric Maxwell-Chern-Simons theory
• The Supersymmetric (2+1)D Noncommutative $C{P}^{(N-1)}$ Model in the Fundamental Representation
• On the duality of three-dimensional superfield theories
• Consistent Interactions of the 2+1 Dimensional Noncommutative Chern-Simons Field
• Supersymmetric non-Abelian noncommutative Chern-Simons theory
• $C{P}^{(N-1)}$ model in aether-superspace
• The 1/N Expansion in Noncommutative Quantum Mechanics
• Perturbative aspects of the supersymmetric three-dimensional massive QED